The show begins with the Royal Translators, our narrators and guides throughout the story. They introduce us to the land of Agrabah ("Arabian Nights/Noches de Arabia").

We arrive at the palace gates, where the citizens of Agrabah have gathered to watch Princess Jazmín pick a husband. While we wait for the Royal Family to appear, the Royal Translators try to get the feel of the city by interviewing a random citizen, Aladdin, and his monkey, Abu. Aladdin tries to tell them how bad things are living in the streets, but the Royal Translators cut him off, not wanting to have bad press. Shortly after Aladdin's interview, the Sultan's Royal Vizier, Jafar, makes an entrance along with his trusty parrot, Iago. As the Royal Translators question Jafar, it becomes clear that both he and Iago are bilingual.

Finally, the Royal Family arrives, consisting of the Sultan, his daughter, Jazmín, and her tiger, Rajah. As the Sultan addresses his people, his Royal Translators repeat his words in the language his citizens can understand. That makes it clear that the citizens and the royalty speak different languages, making communication difficult. The Sultan explains that there are three princes from which Jazmín may choose. As each prince presents himself, it is obvious that Jazmín is not interested in any of them, but the Sultan insists that she must choose a husband.  But Jazmín would rather pick a man whom she loves instead of one chosen for her. Despite her protests, the Sultan and Jafar remind her that she has only one day left to choose a prince. Angry and frustrated, Jazmín uses a momentary distraction to escape from the palace.

Once in the streets, Jazmín runs into Aladdin, who is being chased by the guards for stealing bread ("One Jump Ahead"). They hide from their pursuers together and try to have a conversation when the coast is clear, but this is difficult at first because of the language barrier. However, with Abu and Rajah translating, the two are able to communicate. Aladdin admits his desire to live in a palace and never be hungry again, while Jazmín envies him for his freedom to do whatever he wants. Despite their differences, they are able to understand each other's feelings and begin to fall in love.

Suddenly, the guards return and capture Aladdin and Jazmín, who is forced to reveal her identity to keep from being arrested. However, she cannot stop them from taking Aladdin, as they claim to take orders only from Jafar. Angry at the guards, Jazmín returns to the castle, thinking about the boy she just met ("Un Salto Adelante").

We now find ourselves in Jafar's chambers, where the Royal Translators remark upon the evil ways of Jafar ("Arabian Nights/Noches de Arabia – Reprise"). Iago informs Jafar that Jazmín has returned safely to the palace, and Aladdin has been arrested. While complaining about the Sultan, Jafar reveals that he was the one who divided the land into the royal language-speakers and the street language-speakers by rubbing a lamp. He had hoped that, by making himself bilingual, he would be twice as powerful. However, when he threw the lamp in anger, some dust reached Iago, making him and the other animals of Agrabah bilingual as well. Unfortunately, the lamp is now lost.

Jafar has a new plan. He informs Iago that he added to the ancient laws a new rule: if the Princess fails to choose a husband in the time allotted, the Royal Vizier becomes engaged to the Princess and is consequently the next Sultan. As long as the Princess doesn't fall in love with someone by the next day, she will be forced to marry Jafar. Happy with the plan, Jafar continues complaining about how it has taken this long for him to become Sultan ("Why Me/Pobre de Mí").

Meanwhile, out in the desert, Aladdin and Abu have been locked in a cave because all of the prisons are full ("Arabian Nights/Noches de Arabia – Reprise 2"). However, the cave turns out to be full of all sorts of junk. While looking around, Aladdin finds an old lamp and rubs it, trying to read something that's been written on it. When he does this, the Genie appears, exclaiming that he will grant Aladdin three wishes... with a few limitations, of course ("Friend Like Me/Un Amigo Fiel"). Skeptical, Aladdin remarks that the Genie doesn't seem all that great, and probably can't even get them out of the cave. Using a magic carpet, the Genie helps them escape the cave, only to realize that Aladdin tricked him into doing it without wasting a wish. Still armed with his three wishes, Aladdin wishes to a prince so he can marry Jazmín and speak to her in her own language.

Back at the palace, Jazmín is desperately trying to free Aladdin, but her father is only concerned with getting her married to a prince. While the two are arguing, Jafar enters and announces the appearance of Prince Ali Ababwa ("El Príncipe Alí"). Aladdin introduces himself as Prince Ali, but finds it difficult to get Jazmín's attention. She marches out of the room, angry at everyone for trying to make choices for her. The Sultan tries to cheer Aladdin up while Razu reports to Jafar that their prisoner has escaped from the cave. Jafar and Iago suddenly realize that the lamp must have been in that cave and that Prince Ali is actually Aladdin.

Outside, Aladdin tries to figure out how to get Jazmín's approval. The Genie suggests he try being himself, but Aladdin is sure he just needs to think of the right wish. He asks the Genie what he would wish for, and the Genie tells him how he would wish to be free, rather than be forced to live in a lamp and grant somebody else's wishes. Aladdin suddenly has an idea and rides the magic carpet up to Jazmín's balcony. Aladdin tries to approach Jazmín, but she wants nothing to do with him. However, when she hears him struggle with her language, she is reminded of talking with Aladdin in the marketplace and accepts his invitation to ride the magic carpet. On the ride, she really begins to enjoy spending time with 'Prince Ali' ("A Whole New World/Un Mundo Ideal"). When they return to her balcony, they agree to be married the next day.

As Aladdin leaves the palace, Jafar and his guards stop him, threatening to capture him and throw him off a cliff. Aladdin desperately uses his second wish to make them stop, so the Genie freezes the guards, allowing Aladdin to escape. He accidentally leaves the lamp behind, which is quickly found by Jafar and Iago ("Why Me/Pobre de Mí – Reprise").

The next day, we find ourselves in the middle of Jazmín and Prince Ali's wedding. Sick of pretending to be someone else, Aladdin decides to come clean... and Jafar is only too happy to help with exposing him ("Prince Ali/El Princípe Alí"). The Sultan cancels the wedding, and Jafar comes forward to point out the law that makes him Jazmín's husband and the future Sultan. With his new power, he threatens to kill Aladdin and the Sultan ("Prince Ali/El Princípe Alí"). Jafar rubs the lamp and summons the Genie to fulfill his wishes. Aladdin tricks Jafar into wishing to become a genie, which, because of the rules, traps him inside his new lamp. During this transformation, the Genie's lamp is thrown, covering everyone with magic dust and giving them the power to understand each other.

Finally free of Jafar, Aladdin uses his last wish to free the Genie. The Sultan, touched by Aladdin's sincerity, gives his blessing to Aladdin and Jazmín, allowing them to marry. All is well in Agrabah ("A Whole New World/Un Mundo Ideal – Finale").