Crime Gangs Task Force officers were investigating the incident at the clubrooms last night, police said.
Ambulance crews responded to an assault call at the Middle Row premises at 3.30pm. A spokeswoman said SA Ambulance officers transported a male in his 40s with head injuries.
It follows a string of incidents relating to the outlaw motorcycle gang recently.
Finks member Dylan Jessen was refused bail over an unlicensed, untraceable firearm.
In December, 96 barring orders were administered to Finks and Hells Angels gang members and associates.
In November, a Finks associate, 32 year-old Jason De Ieso, was fatally shot in his Pooraka custom paint and panel workshop.