Several others are feared trapped and personnel from the Ghana National Fire Service and the Police have arrived at the scene to rescue the victims.
He said 11 people were receiving treatment, including one of the school administrators in charge of the trip.
It happened during a storm on Sunday at the waterfall in Kintampo, a popular bathing spot in Ghana's central Brong-Ahafo region.
233livenews.com reported that some students of the University of Energy and Natural Resources were also involved in the accident.
An eyewitness told Ghana's Starr News that most of those involved were students of the Wenchi Senior High School, but that tourists were also injured.
Emergency officials said that the students died when trees, uprooted due to a storm, fell on them while they were swimming in a river near the waterfall.
Parents of some of the victims have flocked to the hospitals at Kintampo to ascertain the condition of their children and for others to identify bodies of their dead relations.
"I have learnt with great sadness [of] the unfortunate incident that occurred at Kintampo Waterfalls yesterday".
The Ghana Tourism Authority said it is working with police and Kintampo local officials to give families needed support and information.
Meanwhile, President Nana Addo Dankwa Akufo-Addo has described as "unfortunate" the accident.