The couple, Ekene Ijokun,40, and Rose Ijokun, 32, who lived at Eleyowo community in Akure North Local Government area, were said to always engage in fight.
They are said to be explaining to police interrogators how their baby died.
Witnesses at the scene could not however state what the fighting parents used to hit the baby.
According to a witness, who claimed to be a sister to the wife, Ekene always beat his wife during pregnancy.
She said: “The baby was strapped to the back of Rose when her husband, Ekene started a verbal attack on her before it resulted into physical combat.
“I didn’t see it as anything as they usually have such fight and make amends after. But this time, it was the other way round as the disagreement degenerated into a physical combat which eventually claimed the life of the innocent baby.
“The baby was hale and hearty before the incident. I removed the baby from her back and placed him on the bed. That was when I realised the baby was lifeless.”
The baby was said to have been declared dead on arrival at the health centre in the community.
Olisa of Eleyowo, Chief Eso Ojo, described the incident as bad saying such a case has never happened in the community.
“Many times, there have been reports on the couple and it’s unfortunate it ended this way.
“I appeal for calm. The case is being handled by the Ondo State Police command.”
Ondo Police spokesman, ASP Tee-Leo Ikoro, could not be reached for comments.