While a stork carries two babies across the sea, the evil Magikoopa Kamek emerges, and attempts to steal both of the babies. Kamek manages to grab Baby Luigi, but Baby Mario falls onto an island in the middle of the sea, called Yoshi's Island, home to all Yoshis. He lands on a green Yoshi, who was apparently taking a walk. The Yoshi clan, accompanying Baby Mario, must journey through the game's six worlds to rescue Baby Luigi and free the stork from Baby Bowser and Kamek. Throughout the game, Kamek tries to stop Yoshi by dispatching his minions all across the island and by using magic spells to transform normal enemies into more powerful creatures that further impede Yoshi's progess.
When Yoshi finally reaches Bowser's Castle, Kamek demands that Yoshi gives back Baby Mario. Suddenly, Baby Bowser wakes up and attempts to ride Yoshi, but Yoshi fights Baby Bowser until the latter becomes unconscious. Kamek then uses his magic to enlarge Baby Bowser to a gigantic size, destroying most of the castle in the process. After being defeated by Yoshi, Baby Bowser is reverted to his normal size and faints. Kamek is horrified and vows to return before flying off with Baby Bowser towards the moon.
Yoshi then frees the captured stork and Baby Luigi. The stork flies the reunited twins far away to the Mushroom Kingdom where their parents live. At dawn, the couple emerges from their mushroom-shaped home to see the pair of infants on their porch.