South Wales Police (SWP) has begun an investigation into allegations of alleged racist and homophobic comments made by players towards a team-mate.
Pontarddulais RFC also reported the "unacceptable" remarks, made on social media to George Mbofana, to the Welsh Rugby Union (WRU).
SWP says it takes such allegations "extremely seriously and it won't be tolerated".
The club said they "will cooperate fully" with any investigations.
SWP said: "We have received a third-party report and officers are attempting to progress the matter with the individual involved.
The west Wales rugby club added: "The players concerned have been suspended until the outcome of the investigation."
A statement from Pontarddulais, who play in Division Two West of the WRU national leagues, read: "Pontarddulais RFC understands that racist and homophobic remarks have been made by players from the club towards another player.
"These remarks are completely unacceptable and have no place in our club, in our sport, or our society and we wholeheartedly condemn them.
"The matter has now been reported to the WRU and the police who are both investigating the matter. The club will cooperate fully with these investigations.
"It is clear that we have work to do as a club. As club officials and management committee we know our initial reaction was flawed. Now is not the time for defensiveness and we are sincerely sorry for causing any additional distress.
"Incidents and language of the sort we have seen here are ugly expressions of deeper prejudices and inequalities, and as a club who is proud of our role in our community it is clear to us that we have a role in tackling those underlying issues.
"We have a duty to our players and our community to make sure our club is a safe, welcoming place and over the next few days we will be seeking guidance from the WRU and others on how we can take meaningful action."
Responding to reports, a WRU spokesperson said: "There is no place for abuse of any kind in rugby union.
"We will make contact with the club in the first instance regarding their internal investigation into the matter."