The UN warned that the latest storm could trigger flash flooding and landslides in Mozambique's far north and the government closed dozens of schools likely to be in the storm's path.
National airline LAM has suspended flights between the capital Maputo and Pemba on the northeast coast because of Cyclone Kenneth, it said in a statement.
The Red Cross warned it was "especially concerned about its possible impact in Mozambique where communities are still recovering from the devastation of Cyclone Idai".
More than 1,000 feared dead in Mozambique storm
Idai was the most powerful storm to hit the region in decades and cut a path of destruction through Mozambique, Malawi and Zimbabwe on the night of March 14-15, causing damage of around $2 billion.
Comoros and Tanzania would also be impacted, added the statement issued by the International Federation of Red Cross and Red Crescent Societies' Africa director, Fatoumata Nafo-Traore.
Cyclone Kenneth passed the Indian Ocean archipelago nation Comoros on Thursday but its effects, including high winds and heavy rains, were still being felt, the country's Meteorological Office wrote on Facebook.
"We must stay alert, avoid touching fallen power cables, wait for permission before driving and keep children at home," it wrote.
An AFP team in the Comoran capital Moroni saw shacks destroyed by the rain and wind, and high seas as a result of the cyclone.
"I have three children, one is small just one month and ten days. We were here until 11 p.m. last night when things deteriorated," a local resident told AFP.
"It was our neighbours who evacuated us."
The UN World Food Programme (WFP) said it was "watching the approaching tropical storm in northeastern Mozambique closely".
"This storm will hit the north and we are expecting that heavy rain will provoke flash floods and landslides impacting the northeastern provinces of Cabo Delgado and Nampula," it said in a statement.
"WFP is working under government coordination and with other humanitarians on an emergency preparedness plan."
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