Ball sort puzzle is a popular logic puzzle consisting of several bins containing balls of multiple colors. Each bin works like a stack; a ball has to follow the last-in first-out order. The player has to sort the balls by color such that each bin contains only balls of a single color. In this paper, we propose a physical zero-knowledge proof protocol for the ball sort puzzle using a deck of playing cards, which enables a prover to physically show that he/she knows a solution with $t$ moves of the ball sort puzzle without revealing it. Our protocol is the first zero-knowledge proof protocol for an interactive puzzle involving moving objects.