The 25-year-old joined the team in November and had four goals and one assist in six games for Red Bull.
The club said on its website on Wednesday that Brassard had assured them last week he would stay.
"Red Bull will be notifying the IIHF of the player's breach of contract and will seek legal advice," the club statement said.
It said Brassard cleared out his locker on Monday and left the next day, despite warnings from club officials.
"He was told not to do anything hasty that he might regret later, and he was reminded in no uncertain terms of his contractual situation," it said.
Red Bull is in ninth place in the Austrian league. The club is led by former NHL head coach Pierre Page and lists NHL players Brassard, Johnny Boychuk and Alex Auld on its roster.
However, the team has had trouble keeping NHL players this season. Brassard, his Columbus teammate Derek Dorsett, Winnipeg Jets defenceman Tobias Enstrom and New Jersey forward David Clarkson have all left shortly after signing.
Brassard's agent Allan Walsh fired back that NHL players left the team because of its "unprofessional" management," saying one player called the club "a joke."
He said Brassard returned home to Ottawa to wait for the NHL lockout to end.Suggest a correction