Police in the southern African country's southern district of Nsanje said the vessel, a canoe, was carrying 37 people across the waterway when the incident took place on Monday morning.
Nsanje police spokeswoman Agnes Zalakoma told AFP locals managed to pull 13 people from the water, while another 23 were still missing on Tuesday.
Rescuers also retrieved the lifeless body of a one-year-old who had drowned in the collision, she said.
"The search mission to locate the missing individuals is currently underway," Zalakoma said.
The canoe started to list and eventually capsized after the hippo collided with it, Zalakoma said.
The Shire is Malawi's largest river.
Boat accidents are common in Malawi, where the lack of regular water transport forces many to cross lakes and rivers in sometimes rickety boats, in the absence of proper regulations.
Last month at least five people died after an overcrowded boat sank in Malawi's central district of Mchinji.
Hippo Causes Fatal Malawi Incident
LILONGWE - A baby died and 23 people are missing after a hippopotamus hit a boat travelling on Malawi's Shire River, authorities said on Tuesday.
