Prince Billy Anaglate, from the fire service, said 18 people died at the scene of the "unusual incident", with a further two dying later in hospital.
Early respondents reportedly used chainsaws to cut off the tree branches before some of the trapped students were rescued.
Eyewitnesses told local police that the incident happened around 4 p.m. (12 p.m. ET) during a severe rainstorm which caused three large trees to fall to the ground.
The former President in a Facebook post, on Monday said "I am keeping the families of the Kintampo falls victims in mind and praying for them".
It is believed many of those who died were students and were swimming when the incident occurred. Other reports put the number of injured...
He said most of the dead are students from the Wenchi Methodist Secondary School and the University of Energy and Natural Resources.
Meanwhile the Minister of Tourism, Arts and Culture, Catherine Abelema Afeku has expressed her honest sympathies and condolences to the families of the victims of the incident.
The Kintampo waterfall is one of the highest waterfalls in Ghana.
Vice President Dr Mahamadu Bawumia has paid a visit to Kintampo in the Bono Ahafo region where a freak disaster at a tourist site has resulted in a tragic loss of 20 revelers.