De Gea limped off with an abductor injury, in Spain's Euro 2020 qualifier against Sweden in Stockholm on Tuesday.
The injury could be a big blow for Manchester United, who are set to meet leaders Liverpool in the Premier League on Sunday.
De Gea has not missed a league game since May 2018.
The 28-year-old had been superb in Tuesday's match, until Marcus Berg nodded home the opener from close range in the 51st minute.
Shortly afterwards, De Gea sat down on the pitch, before being replaced by Kepa Arrizabalaga.
Spain manager, Robert Moreno, said after the match that De Gea tried to play through the pain before being removed.
"He had pain in the abductor muscle but he received treatment at halftime and wanted to keep playing.
"He gave us his word, but in the end he couldn't continue," Moreno told reporters.
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