A suspect is in police custody and is being treated for injuries. Two "heroic" people in the club subdued the attacker, police say.
Club Q, in Colorado Springs, wrote on Facebook that it was "devastated by the senseless attack" on its community.
US President Joe Biden said Americans "cannot and must not tolerate hate".
Police asked people to be patient while they worked to identify victims and finalise the number of casualties, adding that some people had taken themselves to hospital.
Officers received an initial emergency call about an active shooter at 23:57 (06:57 GMT) on Saturday, they said.
The suspect was found inside the club. Two firearms were found at the scene, and the attacker is thought to have used a long rifle.
Police did not suggest a motive for the shooting but said the investigation would consider whether it was a hate crime, and if more than one person was involved.
The FBI in nearby Denver said it was assisting local police with the incident.
Police chief Adrian Vasquez thanked the two club-goers who intervened to stop the shooter.
"Initial evidence and interviews indicate that the suspect entered Club Q and immediately began shooting at people inside as he moved further into the club," he told a news conference on Sunday.
"While the suspect was inside of the club, at least two heroic people inside the club confronted and fought with the suspect and were able to stop the suspect from continuing to kill and harm others. We owe them a great debt of thanks."
Joshua Thurman, 34, was in the club at the time of the shooting.