The club confirmed the signing via their Twitter account on Tuesday.
The Bavarians narrowly won the title this season, edging Borussia Dortmund on goal difference.
Chelsea have progressed to the quarter-finals of the UEFA Champions League following a 2-0 win over Bundesliga side Borussia Dortmund.
The Senegal Football Federation had indicated that Mane would only miss the Teranga Lions’ initial matches at the mundial.
Mane’s injury is a big blow to Senegal who are billed to kick off their World Cup campaign in 13 days.
The supporters were charged with civil disorder, with the police tweeting that many of them were masked and uncooperative.
Xabi Alonso replaced Gerardo Seoane, who was sacked on Wednesday.
Union Berlin coach Urs Fischer, defender Timo Baumgartl and winger Tim Maciejewski have tested positive for COVID-19.
“He broke his hand. The ball hit his hand,” Streich, in his 400th competitive game in charge, said after his team’s 1-0 Bundesliga win on Saturday. “He continued to play.”
With Friday’s win, Bayern top the Bundesliga log with three points and six goals.
