Three members were suspended after the incident in the Long Room, which occurred during the lunch interval after Jonny Bairstow's controversial stumping on the fifth day of the match, which Australia won to take a 2-0 lead in the series.
MCC chair Bruce Carnegie-Brown said members who confronted the Australia players "brought shame" on the club, British media reported, citing an email sent to the organisation's members.
The club will increase the size of the roped-off cordon used by teams as they make their way through the Long Room to their dressing rooms, and restrict members' access in and around the stairwells when teams are coming on or off the pitch.
"During those periods, members will be required to wait at the ground floor or top floor level, with no access to either staircase," Carnegie-Brown wrote.
The new measures will be brought in for the Twenty20 International match of the Women's Ashes series and remain in place for the rest of the 2023 season, when MCC's committee will conduct a review of the pavilion protocols.
"The club will be taking a tougher stance on the general behaviour of members," Carnegie-Brown added. "We expect members not only to heed the words of our stewards in this regard, but to police one another's behaviour."
