An official said 26 people had been rescued so far on Sunday, but it was unknown whether there were any deaths, Al Jazeera reported.
Regional commissioner Albert Chalamila said 43 people – including 39 passengers, two pilots and two cabin crew – were on board the plane.
“As we speak, we have managed to rescue 26 people who were taken to our referral hospital,” Chalamila said. “The rescue operation is still ongoing and we are communicating with the pilots.”
The plane departed from the commercial capital, Dar-es-Salaam, and “fell in Lake Victoria this morning due to storm and heavy rains” in Bukoba.
“We have managed to save quite a number of people,” Kagera province police commander William Mwampaghale told journalists.
“When the aircraft was about 100 meters (328 feet) midair, it encountered problems and bad weather. It was raining and the plane plunged into the water. Everything is under control.”
News reports showed photos of the plane mostly submerged in the lake with only its green and brown-coloured tail visible above the water line.
Speaking to Al Jazeera from Dar-es-Salaam, journalist Faraji Saidi said emergency services were at the scene.
“According to the police commander in Bukoba, the plane crashed due to bad weather, fog. It is raining around that area. Rescue efforts are still ongoing. The airline has worked in Tanzania for so long and has had no crashes,” Saidi said.
Bukoba Airport is on the shores of Lake Victoria, Africa’s largest lake. Rescue boats were deployed and emergency workers continued to rescue other passengers trapped on the plane.
Tanzanian President Samia Suluhu Hassan called for calm during the rescue operation.
“I have received with sadness the news of the accident involving Precision Air’s plane,” she tweeted. “Let’s be calm at this moment when rescuers are continuing with the rescue mission while praying to God to help us.”
Precision Air is Tanzania’s largest privately-owned airline.