Pokémon, despite the whole premise of monsters living inside tiny balls and spitting fire, water and other such elements, does have a foundation mostly based on science. After all, its entire premise is centered around Darwin's theory of evolution -- just an accelerated, more noticeable one. But some moments of the Pokémon Universe have definitely suggested the existence of magic as well.
Witchcraft and Lost Cities
Two big examples of magic within the Pokémon universe can be found in both Episode 74 and Episode 241 of the original anime, respectively. In Episode 74, "The Ancient Puzzle of Pokémopolis," Ash, Misty and Brock discover strange artifacts from a mysterious, ancient city. They meet a young archaeologist named Eve, who explains that the artifacts Ash and friends stumbled upon are relics from the ancient city of Pokémopolis, which was destroyed by an unexplained force of darkness.
As it turns out, said force was a magical Gengar and Alakazam ten times as big as their usual counterparts. The pair were sealed away in the ancient artifacts, then awoken by Ash and friends. These giant Pokémon are completely uncatchable. and apparently exist solely to destroy cities. Even more devastating, they can also paralyze and absorb humans and Pokémon that get in their way. Gengar and Alakazam's reign of terror is only cut short when an equally giant, mystical Jigglypuff is awoken and sings them all to sleep. These artifacts and the legend of these powerful, impossible to catch Pokemon are most definitely a form of magic. The artifacts even float in the air at one point.
In Episode 241, "A Huge Transformation with Pokémon Magic!?," Ash, Misty and Brock encounter an actual witch named Lily. Lily claims to be capable of making a potion that helps one enter the mind of a Pokémon, so the group decides to help her find the ingredients to make said potion. At the end of the episode the potion is finally complete, and Ash volunteers to try it. Lily made a mistake, however, and instead of understanding the minds of Pokémon, Ash literally transforms into a Pikachu. Of course the effects are temporary, so he chooses to enjoy his short time as a Pokémon and use it to play with Pikachu and the others.
Pokemon...Dolls?
More evidence that magic exists in the Pokémon world can be found in Episode 22, "Abra and the Psychic Showdown." In it, Ash encounters the Saffron city gym leader, Sabrina and soon finds out that something isn't quite right with her. Not only does Sabrina possess telekinetic powers, she also constantly carries around with her a living doll that holds part of her fractured psyche, a remnant from the happier days of her childhood. Not only that, but the Gym Leader then transforms both Brock and Misty into dolls and places them in a gigantic doll house... alongside her mother, who was also turned into a doll. If that's not magic, then truly nothing is.
All in all, it looks like the Pokémon world isn't just filled with wonderful creatures with superpowers, but also with straight-up magic, as witches and spells and forces beyond comprehension are canonically part of its universe. This is most likely part of what makes the Pokémon world so enticing and, well -- so magical.