"I have learnt with great sadness, the unfortunate incident that occurred at Kintampo Waterfalls yesterday", Ghana's President Nana Akufo-Addo said in a statement.
The broadcaster said rescue teams used chainsaws to cut through the fallen tree and free those trapped underneath.
Eighteen students died at the scene while two others died in hospital, Mr Anaglate said.
About 11 children are receiving treatment along with the teacher who was supervising them. "Let's also ask the almighty God to heal the injured and receive the souls of the departed into his kingdom".
Desmond Owusu Boampong, a local police commander said almost 20 people have been admitted to the hospital and are being treated.
Some students who had gone to the Kintampo Waterfalls on Sunday on an excursion met their untimely deaths as others sustained severe injuries when hilltop trees fell on them following torrential rains.
Ghana's Tourism Minister Catherine Abelema Afeku has extend condolences to the families of the dead and its prayers for the injured.
"Most of them are students of the Wenchi Senior High School".
"My deepest condolences to the families of all those affected by this unfortunate and tragic incident", he tweeted.
The Kintampo Waterfalls, which was referred to as Sanders Falls during the colonial days, is considered to be the highest falls in Ghana.