A Precision Air plane crashed into Lake Victoria on Sunday before landing in the northwestern Tanzanian city of Bukoba, police said.
According to the police, "bad weather" caused the crash as the plane was flying at about 100 meters (328 feet).
"It was raining and the plane plunged into the water. Everything is under control,'' regional police commander William Mwampaghale told reporters.
Several people rescued
Mwampaghale said rescuers "managed to save quite a number of people."
The AFP news agency reported, citing a regional official, that 39 passengers, two pilots and two cabin crew were aboard the flight.
"As we speak, we have managed to rescue 26 people who were taken to our referral hospital," regional commissioner Albert Chalamila was quoted as saying. "The rescue operation is still ongoing and we are communicating with the pilots."
The domestic passenger plane had departed from the financial capital Dar es Salaam.
Videos on social media showed the Precision Air plane nearly fully submerged, with only the airline's green and brown-colored tail visible above the water.
President urges calm
Tanzanian President Samia Suluhu Hassan sent condolences to "all those affected by the accident" and called for calm.
"I have received with sadness the news of the accident involving Precision Air's plane," she wrote on Twitter. "Let's be calm at this moment when rescuers are continuing with the rescue mission while praying to God to help us."