The students were swimming during a storm when the deadly accident happened, local police chief Owusu Boampong told the BBC.
Twenty-two others were injured and are being treated at local hospitals.
Rescue teams used chainsaws to cut through the fallen tree and free those trapped underneath, local media report.
President Nana Akufo-Addo has tweeted his condolences to the families of the victims.
Police and fire service personnel were involved in the rescue operation at the scene in Ghana's central Brong-Ahafo region, 400km (250 miles) north of the capital Accra.
wn the road.