What is Jupiter's closest planet?

Mars is potentially the closest planet at a minimum distance of 3.68 AU. That varies. Mars would typically be the closest planet, but earth would be closest when earth and Jupiter are on the same side of the sun and Mars is on the opposite side.

At 10 AU, Saturn would almost always be further from Jupiter than Mercury or Venus. When Mars and Jupiter are on opposite sides of the sun, the distance between them is eight AU, whereas the distance between Jupiter and Saturn when they are lined up on the same side of the sun is 5 AU. That means when even earth (1 AU) is on the opposite side from Jupiter and Saturn (Jupiter and Saturn are in daylight), Saturn would be slightly closer.

Most of the time, however, Mars would be the closest planet to Jupiter.