In a distant Middle Eastern Kingdom, the young Aladdin lives with his nearsighted and stubborn uncle, Abdul Azziz Magoo, who owns a lamp shop. Believing that Aladdin is growing up to be a lazy and irresponsible man, Magoo encourages Aladdin to get married. Meanwhile, the wizard Wazir has been siphoning money from the royal treasury and manages to persuade the now-bankrupt Sultan to ask his daughter, the Princess Yamina, to marry the richest man in the land - which now happens to be Wazir. During a royal procession, Aladdin and Yamina fall in love. In his quest for absolute power, Wazir seeks the genie of the magic lamp, which is sealed in a magic cave, and needs Aladdin to get it for him. However, he is unable to obtain the lamp after it falls back into the cave with Aladdin still inside. Aladdin meets the genie and escapes the cave with a chestful of treasures. Magoo then takes the treasure to the palace as a dowry, and manages to unintentionally spoil Wazir and Yasminda's wedding with his naivety and nearsighted physical handicap. The genie conjures a palace and wealth for Aladdin, which is enough to persuade the Sultan to agree to let Yamina marry him. However, the vengeful Wazir manages to steal the lamp and the allegiance of the genie, thus exposing Aladdin as a fraud. Aladdin is sent to the scaffold. As Wazir kidnaps and attempts to woo Yamina back, the clueless Magoo inadvertently manages to obtain the lamp from Wazir and thus the allegiance of the genie, while also managing to dodge all of Wazir's attempts to kill him. Wazir falls to his death. Only wanting the best for his nephew, Magoo wishes for Aladdin and Yamina to live happily ever after; thus, the genie saves Aladdin from execution and he and Yamina wed.
The film was originally directed by Pete Burness, who was the series director on the popular series of Mr. Magoo theatrical cartoons produced for Columbia by UPA between 1949 and 1959. Disagreements with producer and UPA owner Stephen Bosustow led to Burness resigning and Bosustow recruiting Jack Kinney, the director of many of Disney's Goofy cartoons, as the film's new director. The voice of Magoo in the short cartoons, Jim Backus, reprises his role in the feature, with Katheryn Grant, the singer/actress wife of Bing Crosby, as the voice of Princess Yasminda and Dwayne Hickman, from TV's The Bob Cummings Show and The Many Loves of Dobie Gillis, as the voice of Aladdin. 1001 Arabian Nights was the first full-length feature produced by UPA, a studio which had revolutionized animation during the 1950s by incorporating design and limited animation. The film was not a box-office success, and was UPA's final release through Columbia, which had ended its distribution for the UPA short subjects in favor of lower-cost Loopy De Loop cartoons from Hanna-Barbera Productions. Following the film's release, Bousustow sold UPA to Henry G. Saperstein, who moved the studio into television production and a second feature production, Gay Purr-ee, before closing the animation studio and moving UPA on to other ventures.