Law and Home Affairs Minister K. Shanmugam has described Facebook user Thomas Chua as "smug", and his post gloating over the death of 29-year-old Staff Sergeant Nadzrie Matin as "sick".
The Traffic Police outrider died in a traffic accident in Serangoon Road on Thursday while on duty.
Mr Chua claimed he had previously received a speeding ticket from Staff Sgt Nadzrie.
His Facebook page, which has since been deactivated, also hosted a video of the fallen officer.
In a post on his Facebook page yesterday, Mr Shanmugam said: "I was deeply upset and angry about a gloating post that one Thomas Chua has made on police officer Nadzrie's death. Nadzrie died while on duty.
"Thomas was gloating about Nadzrie's death, because Nazdrie had given him a ticket!
"People like Thomas are sick in the head. No decency or any sense of right and wrong."
Mr Shanmugam said it is "because of officers like Nadzrie that the rest of us have safety and security".
"Thomas' comments are an insult to all police officers, and deeply offensive to Nadzrie's family."
Mr Shanmugam added: "You wonder what human decency people like Thomas have - to be so self-centred, smug and making nasty remarks about an officer who died doing his duty. While there is a completely distraught wife, grieving parents and family, and teammates who are crying."
He had also shared a separate post on Thursday, dedicated to Staff Sgt Nadzrie. Written by Mr Karthik Vinod, it spoke about the grief felt by all police officers.
Mr Vinod also stood up for the Home Team, saying that officers work long, laborious hours and put their lives at risk to protect the people of Singapore.
Mr Vinod's post has garnered more than 2,400 likes and 1,800 shares. It was one of many tributes made to Staff Sgt Nadzrie, who joined the force in 2009.
On Facebook, some have changed their profile photos to show a horizontal blue stripe across a black-and-white Singapore flag or black background in tribute to him.