Fisher will not play in Thursday's game against the Miami Heat, and also won't travel with the team on a two-game road trip through Memphis and San Antonio this weekend.
Fisher, 38, injured the tendon in the first quarter of Tuesday's win over the Philadelphia 76ers. He will be re-evaluated next week, and no timetable for his return has been set.
Fisher has played in all nine games since signing Nov. 29 with the Mavericks. He is averaging 8.6 points and 3.6 assists in a little more than 25 minutes per game.