Jordan Tapping, who plays for East Stirlingshire, was substituted after suffering "extreme distress" caused by comments at a Scottish League Two game in Peterhead yesterday.
The club said in a statement: "Peterhead FC took immediate steps to identify the culprits and Jordan received a personal apology from their chairman, Rodger Morrison.
"East Stirlingshire FC will lend every assistance possible to Peterhead FC in trying to pick out those responsible.
"Furthermore, the club will be contacting the SFA and the Scottish Professional Football League to highlight what has happened and to urge them to take whatever steps are necessary under their rules to deal with the matter."
A Police Scotland spokesman said: "Following media reporting of the racial abuse of an East Stirlingshire player by some fans during the match against Peterhead Football Club at Balmoor Stadium, Peterhead, on Saturday, Police Scotland can confirm that a criminal enquiry has been launched into the matter.
"We will be liaising closely with both football clubs to thoroughly investigate this incident which, at this time, would appear to have involved a small minority of people.
"We ask any supporters who saw or heard anything of a racist nature to get in touch with Police Scotland on the non-emergency number 101."