Tanzania's Lindi, Mtwara and Ruvuma regions have been listed as the most prone to the weather, which is predicted to hit the country on Thursday.
Authorities have urged people who live in mud houses to seek shelter where they would be safe.
The storm is forecast to also affect Mozambique's northern Cabo Delgado province.
Red Cross and Red Crescent volunteers have been put on alert in Tanzania and Mozambique. And the organisation has alerted communities in northern Mozambique most likely to suffer from flooding and landslides.
Authorities in the island nation of Comoros have closed airports for at least 24 hours as a precautionary measure against the cyclone expected there on Wednesday, reports privately-owned Comores Infos news website.
Schools have also been closed, it adds.
Cyclone Kenneth could be the strongest cyclone ever recorded to make landfall in this region, BBC Weather reports.
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