Broncos head coach John Fox said Warren, who signed with the team earlier this month after being released by New England, suffered a triceps strain. He said Thomas suffered a strained pectoral muscle.
The Denver Post reported an MRI showed Warren's injury to be a partial tear, which may require surgery, and that Thomas will miss the rest of the preseason.
Warren, 30, missed all of last season with a hip injury suffered during the preseason. He had been with New England since 2003, and was a full-time starter since '04.
Thomas re-signed with Denver this offseason, returning to the team that picked him in the fourth round of the 2007 draft.
Also on Tuesday, the Broncos released running back LenDale White and waived linebacker A.J. Jones.
White signed with Denver last offseason, but he missed the entire 2010 season with a torn Achilles tendon. He was released to give younger running backs an opportunity, according to Fox.
White, 26, has rushed for 2,349 yards and 24 touchdowns in 58 career games -- all with the Titans.
Jones signed with the Broncos as an undrafted free agent.