Japanese moviegoers are famously well-behaved, even carting out their empty soda cups and popcorn containers after the screening. They also tend to make few sounds beyond titters for comedies or snuffles for tear-jerkers.

But the full-house crowd at the Feb. 5 world premiere of the animation “Hypnosis Mic – Division Rap Battle” at Toho Cinemas Hibiya cheered, applauded and waved multicolored light wands as the on-screen action unfolded.

The 300 fans, who had been selected by lottery, were already excited by the presence of the film’s voice actors and director, Tsujimoto Takanori, on stage prior to the screening in the trendy Tokyo Midtown shopping and entertainment complex. But another, more important reason for their audible enthusiasm was the film itself, the first Japanese feature to be fully interactive. Prior to the start of the story, set in an alternative future where the women who rule central Tokyo have channeled male aggression into rap battles,...