Branch suffered the injury in the first quarter of Sunday's 19-9 victory over the Jacksonville Jaguars.
Raiders coach Dennis Allen, who referred to the injury as "significant" on Sunday, would not comment on the exact nature of the injury during his Monday media conference.
"He's probably going to miss some time," Allen said. "How much that time is, I don't know."
Branch, the Raiders' highest-paid player this season at $9.5 million, was injured while rushing Jaguars quarterback Chad Henne on a third-and-7 play.
Brandian Ross and Usama Young replaced Branch. With Charles Woodson starting at free safety, Allen has a choice to make -- move Woodson to strong safety and start Young at free safety, keep Woodson at free and start Ross at strong or mix and match throughout the game.
The Raiders also have a safety on the practice squad in Shelton Johnson.
"Listen, if Ty's out a while, then we've got guys that we feel like can step up and make plays, whether it's strong safety, free safety," Allen said. "To me, I look at those as interchangeable positions and they really need to be to have the flexibility to do some different things defensively.
"I think I've got confidence in all three of those guys that are back there."
The other Raiders player to leave Sunday's game due to injury was left guard Lucas Nix, who injured an ankle. He was scheduled to have an MRI of the injury Monday afternoon. Andre Gurode replaced Nix in the third quarter.
Branch is one of just two returning starters on defense for the Raiders, along with defensive end Lamarr Houston.
ESPN's Adam Schefter and ESPN.com's Paul Gutierrez contributed to this report.