Tillman (knee) has been ruled out for Tuesday's game against the Nets, Taylor Snow of the Celtics' official site reports.
Tillman was traded from the Grizzlies to the Celtics on Wednesday but hasn't yet been able to make his team debut due to his knee injury. It wouldn't be surprising to see him remain sidelined for Wednesday's rematch against the Nets to give him additional time to rest before the All-Star break.