Trouble erupted after Collins and Dunne were critical of some of manager Gerard Houllier's coaching staff during a team break at a Spa in Leicestershire, according to The News of the World.
Then incident reportedly occurred at a dinner, held in a private room and restricted to the first-team squad and coaching staff, following a paint-balling session.
"I apologise unreservedly for my behaviour on Wednesday night. It was not acceptable and I am genuinely sorry," Dunne told the newspaper.
Collins added: "We were wrong. This should not have happened and I apologise for the part I played."
The club are now due to launch a review of the incident, with a spokesman adding: "We have launched an investigation in line with our internal disciplinary procedures."
Villa manager Houllier has had to deal with a number of disgruntled players since taking over from Martin O'Neill at the start of the season and has shipped out both John Carew and Stephen Ireland following disagreements.