Personnel of the Ghana National Fire Service and the police service are now at the scene to rescue those trapped under the fallen tree.
The broadcaster said rescue teams used chainsaws to cut through the fallen tree and free those trapped underneath.
They were swimming during a storm when the freak accident happened, emergency officials said. "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.
The students and teachers, numbering 63, and a driver were from the Wenchi Methodist Senior High School in the region.
Ghana's Tourism Minister Catherine Afeku expressed sympathies to the families of the victims and said the injured are at local hospitals.
Eyewitnesses say the trees fell from the top of the waterfalls and landed on the people, mostly students engaging in local tourism.
Kintampo waterfalls - one of the highest in the country - is located in Ghana's Brong Ahafo region, around 400 kilometers (almost 250 miles) north of the capital, Accra.
About 11 children are receiving treatment along with the teacher who was supervising them.
President Nana Akufo-Addo has tweeted his condolences to the families of the victims.