During the 2-2 draw with Ayr United, which proved to be manager Gus MacPherson’s last as manager, a man and a woman were kicked out amid claims a player was subjected to abuse from a section of his own fans.
The club has now pledged to investigate the alleged racism and called on fellow supporters to help the probe if they witnessed the incident.
A statement from the Championship club read: "The club is aware of an alleged incident of racial abuse being shouted from the home support at one of our players during Saturday's match against Ayr United at Cappielow.
"We are aware that a male and female were ejected from the stadium during the game.
"Racism has no place in football, or wider society. As a club, we condemn all forms of racism, and any racist behaviour will not be tolerated."
The statement also requested any potential witnesses contact the club via email.
A late equaliser from the visitors drew the scores level 2-2 and ultimately cost Gus MacPherson his role as boss in Greenock, with the Ton eighth in the table, and still a point behind the Honest Men.
Ayr United are also investigating their own travelling supporters after a smoke bomb was thrown onto the pitch during goal celebrations at the game.
A club statement from Somerset Park read: "The club would like to thank our supporters for coming to Cappielow on Saturday to support the team. Unfortunately, the behaviour of a small few fell well short of acceptable conduct.
"Setting off smoke devices may seem like it’s ‘harmless fun’ and ‘adding to the day’ however this is far from the case and in actual fact affects the health of players and other supporters.
"In circumstances where any of our supporters, or individuals who are associated with AUFC, are accused of unacceptable behaviour we will carry out a rigorous investigation to establish the facts of the situation.
"We are very proud of our loyal support and whilst the vast majority share our views we urge everyone to be respectful of all others at all times.”