Jordan Tapping, who plays for East Stirlingshire, was substituted after suffering ''extreme distress'' caused by comments at a Scottish League Two game in Peterhead on Saturday.
Police Scotland said the incident was an "isolated occurrence" and have launched an investigation.
The force appealed for anyone with information to contact them.
Inspector Andy Imray said: "We are working closely with Peterhead Football Club to identify those responsible for this abuse and I would like to thank those people who have already contacted the club about this. I hope this encourages other people who have yet to come forward to do so as soon as possible.
"From information gathered so far, we have positive lines of inquiry to progress.
"The match itself was not policed, in line with appropriate assessment between the police and the club. I consider this unacceptable incident to be an isolated occurrence, which will be fully investigated. The policing of future matches will be determined on an intelligence-led basis, informed through liaison with Peterhead FC and visiting teams."
The match, at Balmoor Stadium in Peterhead, was won by Peterhead 4-0.
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.''
In a statement on its website, East Stirlingshire FC said: "Jordan, his family and the club would like to place on record our thanks to those people from the Scottish football world and beyond who have been in touch since Saturday to offer messages of support.
"However, a criminal investigation is now under way and we feel it would be inappropriate to comment any further while this is taking place.
"Jordan and the club have an important match to prepare for against Stirling Albion on Saturday. We will co-operate fully with Police Scotland while trying to retain our focus on getting ready for our next game."
A Scottish Professional Football League (SPFL) spokesman said: "The SPFL has this afternoon received and reviewed the referee's match report from the Peterhead v East Stirlingshire game on Saturday March 1.
"We will now conduct a full investigation into an alleged incident at that fixture and will be speaking to both clubs, match officials and Police Scotland."