Last month, Cyclone Idai caused hundreds of deaths in the region. More than 1,000 people died when the storm brought devastation to Mozambique, Malawi and Zimbabwe.
At least three million people were left in need of humanitarian assistance.
Kenneth made landfall on the north coast of Mozambique on Thursday evening, with wind speeds equivalent to a Category 4 hurricane.
There is no previous record of hurricane-force systems ever hitting the region so far north before, BBC Weather reports.
It is expected to weaken as it moves inland.
A "compulsory evacuation" of families is underway and will continue "until we have all people in secure ground", INGC spokesman Paulo Tomas said.
More than 680,000 people are said to be at risk from the cyclone, Mozambican officials said on Wednesday. Flights have already been cancelled and schools closed.