Shaw was a passenger in a car which was pulled over by police in Malvern Rd, Toorak. After a verbal altercation with police, he was taken to St Kilda police station.
He received a $590 penalty notice for drunken behaviour and was released on Saturday morning without charge.
Chief Executive David Matthews said: "We have spoken to Heath about his behaviour and his responsibilities as a member of our leadership group.
"He accepts that he let himself down on this occasion and that his behaviour was unacceptable. We are disappointed with what happened and so is he and we have agreed that he will undergo counselling.
"We have also agreed to consider the matter further when he returns to the club after his current leave period."
The club has informed the AFL about the matter and will be making no further comment at this stage.
