The holes, measuring one to three metres deep, appeared in the Trang B area of Tri An Ward when water levels in the reservoir fell earlier this month.
Local residents said they could be craters left by bombs dropped during the war.
The area is frequented by residents, children and tourists for fishing, sightseeing and camping, raising safety concerns.
Local military authorities said no unexploded ordnance remained in the area, but warned that the deep holes still posed a safety risk.
After several days of heavy rain, rising water levels have submerged the holes again, increasing the risk of accidents as they are no longer visible.
Authorities have installed warning signs and urged residents and visitors to stay away from the area to prevent drowning and other accidents.
Visitors have also been advised not to swim, fish or camp near the affected area.