The scuffle involved team members, drivers and others in the immediate vicinity following Sunday's race, while cars were returning to their berths.
Team Penske and Andretti-Green Racing have both been fined $25,000 for unsportsmanlike conduct. Drivers Tony Kanaan (Andretti-Green Racing) and Sam Hornish Jr (Team Penske) have also been punished with an undisclosed amount, as per the sport's rules.
Kanaan struck Hornish when the pair returned to the garages after the chequered flag. Hornish had squared up to his rival, accusing him of a shunt on entry to the pit lane, supposedly revenge for a collision during the race.
IndyCar ready to welcome back spectators
19/06/2020 AT 15:09
Hornish's father Sam promptly shoved Kanaan and has therefore been banned from the pit lane for next weekend's race at the Nashville Superspeedway.
Anthony Fedele, a friend of Andretti-Green co-owner Michael Andretti, tackled the 65-year-old parent and has been suspended from closed areas indefinitely.
"We are disappointed in the actions of the drivers, the team members and the non-team members involved in the incident," said governing body president Brian Barnhart.
"Entering the 'field of play' even after the checkered flag and actively becoming engaged in anything outside of celebration is inappropriate and inexcusable.
"We believe that emotions play a role in our sport but it is unfortunate that others took it as an opportunity to become involved. We have spoken with both drivers and believe them when they said that there was never going to be physical contact between them.
"Safety is a priority, and while we do not condone incidents like Sunday's, it was an even more precarious position with cars still running at pit speeds."
Will Power first Australian to win Indy 500
27/05/2018 AT 23:24
Andretti: ‘What will propel Indycar into future’
07/04/2018 AT 19:02