He used the word "a-hole" to describe someone on radio because he was irritated by the "constant complaints" of a visually-impaired person on Facebook.
Then, his fellow DJ went all the way and called him an "a** hole" for using that word. The use of such strong language surprised some listeners of Class 95FM.
The Media Development Authority (MDA) said it had been notified and is "reviewing the case".
The incident happened during the Morning Express show on Thursday, a radio programme hosted by DJs Joe Augustin and Glenn Ong, both 44.
During a 40-minute segment, the pair, known to ham it up for radio by taking opposing views, engaged in what appeared to be a heated discussion over the actions of Ms Cassandra Chiu, who is visually impaired.
Ms Chiu, who is one of the Singapore Woman Award 2012 winners, had posted on Facebook that she had been denied service at a McDonald's outlet in Jurong Park on Monday after she had walked in with her guide dog Esme.
Ms Chiu, who began to lose her sight at age eight due to a degenerative eye condition called Stargardt disease, has a Facebook page called Esme The Guide Dog in which she writes as Esme.
After her encounter at McDonald's on Monday, she had posted on Esme's account: "They just refused to serve us because it's free muffin day and blind people are not entitled."
Her generalisation and presumption of what took place had upset Augustin.
Ms Chiu is known on Facebook for being rejected at local establishments here such as clothing store Forever 21 in 2012 and ice-cream shop Haagen-Dazs last year because Esme was perceived as her pet and was not allowed the shops.
While discussing her latest post, Augustin then called Ms Chiu an "a-hole" for her constant complaints and "inflammatory remarks" that the visually impaired were being discriminated against and denied McMuffins at McDonald's. Ong then appeared to be offended, and called him an "a**hole" for calling Ms Chiu that.
Listeners were then called in to give their opinions on whether they agreed with either DJs over Ms Chiu's Facebook post.
Ong told The New Paper: "I was shocked that Joe would say this about someone as well-regarded as Cassandra. I think she was justified and she had every right to kick up a fuss.
"Cassandra and Esme's latest encounter was a brush with stupidity, as far as I'm concerned.
"I mean the law allows seeing eye dogs everywhere, yet she has to work so hard to make establishments realise this. I think this latest episode was the straw that broke the doggy's back."
Augustin, on the other hand, told TNP: "What happened (Ms Chiu being refused service at McDonald's) should not have happened.
"But what I was vocal about was what I thought of Cassandra's constant complaining.
"For me, it was the action and manner in which the subject was broached on her dog's Facebook page that was too much."