Conservative group leader Nadeem Ahmed contacted the force on Thursday morning after a comment containing an alleged racial slur was made on a Facebook page.
Officers said they would talk to Coun Ahmed, who has been the opposition leader on Wakefield Council since 2015, to get more details.
In a statement, West Yorkshire Police said: "Police were called at about 10.52am this morning (Thursday) by a caller from the Wakefield area reporting hate comments made via on social media
"A hate incident has been logged and officers will be speaking further with the caller to get more information."
Coun Ahmed said there was "no place" for the language used.
He said: "What's been used is a derogatory term, and it did really upset me. The comments should be deleted.
"I've no problem with people disagreeing me. If they've got an opinion that's fine, but this is stooping to a new low.
"Since I was elected as a councillor in 2006 I've seen some heated arguments, but those should never descend into racism, sexism or homophobia.
"When things like this happen, it's no wonder people aren't putting themselves forward to be councillors."
Local Democracy Reporting Service