White was injured in the Spurs' win Monday in Washington. The fourth-year guard is averaging a career-best 15.4 points this season for San Antonio, which played 18 of its first 19 games this season without White because of a toe injury.
"You can imagine his spirits are not high," Popovich said.
San Antonio was at Miami on Wednesday night, losing 116-111.
White is not expected to require surgery. Rookie guard Devin Vassell will take White's place in the starting lineup, Popovich said.
"When he gets minutes, he's played well," Popovich said of Vassell, who scored 11 points Wednesday night in his second start.