Investigators are trying to determine where the gun, left unattended in the house, came from, Cleveland.com reported, citing police.
The baby boy was rushed to a hospital but could not be saved.
His mother could be heard screaming on the back porch after she was told her son had died, reports said.
“It’s a sad day for Cleveland,” newsnet5, an ABC affiliate, quoted Cleveland Police Chief Calvin Williams as saying.
“This fascination we have with handguns, not just in the city, but in this country has to stop. This is a senseless loss of life in this city again.”
The person responsible for bringing the weapon into the home and leaving it where a small child could get to it will likely face charges, Williams said, adding that at least one adult was home when the tragedy happened.