The striker was stretchered from the field early on his first international start and faces several weeks of rehabilitation.
The striker, making his first start for the Three Lions, was withdrawn after 33 minutes against Republic of Ireland after appearing to roll over on his ankle and being stretchered from the field.
"He's not going to [play] Brazil, unfortunately," Hodgson told ITV. "It's ligament damage, we think. We are not 100 percent sure. I fear it will keep him out for a few weeks. The surgeon is with him now and he will be contacting Liverpool [shortly]."
Sturridge went into the game in fine form for Liverpool, scoring six goals in his previous five outings, and Hodgson lamented the injury hampering the striker's impressive start at Wembley.
"He had a brilliant start to the game and we were really sad to lose him," Hodgson continued. "I think we missed him as Jermain Defoe hasn't played for a while and is also suffering from a slight injury problem."
Jermain Defoe replaced the Liverpool man on the night, but will face competition from Wayne Rooney and Danny Welbeck for a starting berth to face the five-time world champion.