The trio were captured on video arguing with door staff at a nightclub in the city, with Herd kicking the club’s glass doors during the scuffle, which took place just hours after Villa’s player of the year awards evening.
The news comes as Alex McLeish’s side prepare for a crucial Premier League game against Tottenham at Villa Park on Sunday, with their status in the division still not assured for next season.
The players have apologised to the club and their supporters, while all have been fined, with the proceeds going to charity.
An Aston Villa statement said: "The club dealt with this matter internally on Tuesday and the players in question have been disciplined, with the fines being split between two charities the club are promoting at the game against Spurs on Sunday - Cure Leukaemia and Anthony Nolan.
"Our players attended the club’s end-of-season dinner on Monday night and training on Tuesday was limited to players who did not start in Saturday’s Premier League game against West Bromwich Albion and those not carrying injuries.
"As a club, players, management and fans are completely focused on Sunday’s game against Spurs at Villa Park."
Aston Villa manager McLeish believes the behaviour of Delph, Herd and Collins is a "slur on the club".
He said: "I feel for (club owner) Randy Lerner and the fans of Aston Villa Football Club but the players need to show some respect for themselves and the football club."
In official statements, the players have all apologised for their conduct.
"I’m sorry for what has happened and I take responsibility for my actions,” Wales international Collins said.
"It does not show me in a very good light and does not put the club in a very good light. I know I should not have been out in a club with my wife after the end-of-season dinner at that time in the morning and I was wrong to be in that position."
"It was no one’s intention to get involved in any trouble but I realise that my actions on the night were not acceptable,” 23-year-old Herd added.
Former England Under-21 international Delph said: "I’m sorry for being out on Monday night, the early hours of Tuesday morning and I apologise to the club, the fans, the chairman, the manager and my colleagues.
"I am injured, I won’t be fit again until pre-season and I probably thought that going out would not carry any consequences.
"I was sober, I was in control of my actions and I did try to calm down the situation.
"I didn’t hit out or strike anyone but I should not have been there and I was wrong to be in this position.”