The company said it was "grateful that no harm was caused to any of our staff or members."
The man was arrested after trespassing and refusing to cooperate with requests to leave the gym, police said in a statement this afternoon.
Christchurch resident Charann Poinga uploaded the video to Facebook.
Early in the video, a policeman appears to take a swing at the man.
The man was restrained by several officers and then appeared to yell: "At the end of the day, you just whacked me in the head for nothing. You whacked me in the head for nothing. I didn't do nothing. What's up?"
However, Inspector Erasmus said today the "brief footage on social media, at just over 1 minute long, does not reflect the full context of what occurred, nor does it capture the threatening and aggressive behaviour witnessed beforehand by gym staff and police".
The incident happened on Tuesday, police said, when the man, who was not a gym member, allegedly gained entry by "tailgating" a member.
He then man acted erratically and appeared to be impaired, police said.
"Given the man's aggressive behaviour and the possibility of a weapon, such as a piece of gym equipment, being used police were concerned for both their own safety and that of others nearby," Mr Erasmus said.
"After further discussion the man began walking towards the exit, escorted by police, but then stopped and became aggressive towards one of the officers. It was at this point that the officer swung his arm around the man to place the him in a front headlock, which enabled police to take to the ground in a controlled manner."
The gym security footage gave a clearer angle than the one filmed by the gym member and uploaded to Facebook, police said.
Ms Poinga was invited to view the security footage at the station to allay any concerns she might have, police said.
"The security footage clearly shows the officer swinging his arm to trap the man in a front headlock, who is then pulled forward into the officer's body and taken to the ground, with other staff assisting in the arrest."
The man was then taken to a police station, given a pre-charge warning and released, police said.
The Independent Police Conduct Authority was advised of the incident.