Quinn is in stable condition, the team announced in a statement.
"Things look encouraging," Rams coach Jeff Fisher told ESPN.
The 26-year-old Quinn was diagnosed with a brain tumor in high school, a condition that caused intense headaches until doctors drained excess fluid from his skull, according to the Orange County Register.
"Highly unlikely," Fisher said about Quinn's hospitalization being related to the tumor.
The 6-foot-4, 264-pound Quinn, a first-round draft pick (14th overall) of the Rams in 2011, has recorded eight tackles and two sacks in seven games this season. In six seasons with the Rams, he has 184 tackles and 52 sacks in 78 games.