The victims, part of a family of 21 in a village in the northeastern region of Kavango East, fell ill after dinner on Saturday and were rushed to hospital, police said.
Local media reported that the deeply impoverished family had eaten porridge made from cereal residues left from brewing an alcoholic drink.
As of Wednesday, 15 had died, police spokesperson Kauna Shikwambi told AFP.
"So far this is the biggest number of deaths suspected to be from the ingestion of possible toxic material," Shikwambi said.
An investigation has been opened, with results awaited from autopsies and lab tests, she added.