Dumervil, 28, faces a charge of aggravated assault with a firearm, which court records show is a third-degree felony.
The Denver Post reported Dumervil was released from jail Saturday after he posted $7,500 bond.
The circumstances surrounding his arrest were not immediately available.
"No charges have been filed. No aggravated assault or assault took place. And it is likely that once the full investigation is complete, no charges will be filed against Mr. Dumervil," Harvey Steinberg, Dumervil's attorney, told ESPN NFL Insider Adam Schefter.
A spokesman for the Denver Broncos said that the team is aware of the matter and continuing to gather facts.
"This is a very serious allegation, and we will thoroughly review the details while the legal process runs its course," the spokesman said a statement issued by the team.
Dumervil, a Miami native, had 9½ sacks in 14 games last season after sitting out 2010 due with a torn pectoral muscle. The former fourth-round pick led the NFL with 17 sacks in 2009.
The Broncos drafted Dumervil out of Louisville with the 126th overall pick in 2006.
Information from The Associated Press contributed to this report.