NBA Official -- Cavs Video Is Offensive ... 'No Place In Our League'

The NBA tells TMZ Sports ... league officials have contacted the Cleveland Cavaliers about their "inappropriate and offensive" arena video and told the team it was completely UNACCEPTABLE.

The team has been under fire over the video -- which shows a male Cavs fan slamming his GF to the ground when he finds out she's a Bulls fan. It's about as domestic violencey as it gets.

Now, an NBA spokesperson tells TMZ Sports ... "We agree with the Cavaliers that the video shown last night was inappropriate and offensive."

"We spoke to the team earlier today to convey our disappointment. Anything that makes light of violence of any sort has no place in our league or society."

The team has since pulled the video off its website -- and called the thing a big mistake.