Relatives rushed him to St Luke's Hospital in rural Lupane district but he died at noon because there was no anti-venom to treat him.
"The whole of Lupane has no anti-venom medicine," the newspaper said.
"There was nothing much the boy could receive as treatment."
Black mambas are among the deadliest snakes in Africa. A bite can kill in hours.
Anti-venom exists for black mamba bites but it is not widely available in Zimbabwe.
Cases of patients surviving if they are put on a life support system have been recorded in the region.
A man died at the same hospital last week after a puff adder bite, the Southern Eye reported.
--Sapa--