The Croatia international suffered the injury in Tuesday's 3-2 Champions League defeat at Olympiakos Piraeus and was operated on successfully in Madrid on Thursday, Atletico said on their website (www.clubatleticodemadrid.com).
"He is planning to start training on Sunday or Monday," club doctor Pedro Luis Llopis was quoted as saying in local media.
"Normally he would be available to play in 15 days but with a mask he could do so in 10," Llopis added.
"He will have a personalised mask, the smallest and most comfortable possible, although it's always difficult to play under those conditions."
Mandzukic, who joined Atletico from Bayern Munich in the close season, will miss Saturday's La Liga game at home to Celta Vigo as well as Wednesday's trip to Almeria.
He should be back for the Champions League Group A match at home to Italian champions Juventus on Oct. 1.
Coach Diego Simeone said he was planning to deploy two of Atletico's other new signings up front on Saturday, France forward Antoine Griezmann and Raul Jimenez of Mexico.
"He (Mandzukic) is a good lad," Argentine Simeone told a news conference.
"He is hugely magnanimous and has incredible physical strength," he added. "We hope he recovers soon and can be back with us."
(Reporting by Iain Rogers, editing by Toby Davis)
