The 6-foot-3, 190-pound Hudson averaged 12.7 points, 3.5 rebounds and 2.7 assists in 13 games for the Cleveland Cavaliers this season. He scored a career-high 26 points on April 8 at New Jersey.
Grizzlies coach Lionel Hollins says "if he can come in and help us for one game or two games in the playoffs it's always good."
This is Hudson's second stint with the Grizzlies, having appeared in nine games as a rookie in 2009-10. Hudson was drafted in the second round by the Boston Celtics in 2009.
Hudson is inactive for Friday night's game at the Charlotte Bobcats.