Cipriani met with senior club officials and management on Tuesday and apologised for his actions, stating that he would suspend himself if he is involved in any further trouble.
"I regret any embarrassment my behaviour has caused," said Cipriani, whose high-profile move to Super Rugby's newest franchise had already created plenty of headlines.
"I am looking forward to putting this incident behind me, focusing on my rugby and contributing positively to the team's culture.
"As my behaviour was not in line with our pledge, if anything else happens along these lines again, I have agreed with the players that I will stand down for an appropriate period of time."
"We're all disappointed but I think it's been handled well," said Macqueen.
"The players supported the club and they've worked with Danny on it. I'm pleased that it's been done in this way because Danny and the players are now working together - the players haven't separated themselves from Danny.
"We'll be treating every one of the players equally and we'll be treating them as adults. If they don't behave like adults then the repercussions will come."
Cipriani has enjoyed a mixed start to life in Australia on the field, having moved from zero to hero in the space of a week.
The England fly-half was benched for the opening match of the season - a 43-0 defeat by the Waratahs - before kicking six penalties, including a last-minute winner, against the Brumbies in Round 2.