The National Emergency Operations Center, which has declared the highest red alert for coastal districts, said there was a serious threat to shipping in the Mozambique Channel and told all fishing boats and other vessels to stay out of the sea.
Belarmino Chivambo, spokesman for the National Institute for Disasters Management, said one person died in the northern coastal town of Moma and another four in Mogincual, further north.
The cyclone has wreaked havoc on Mozambique Island and Nampula province in the north and the central Zambezia province. Zambezia was badly affected by earlier flooding - the worst since 2001 when 800 people died. With the flood waters slowly subsiding, there are fears the cyclone will bring new devastation.
The National Emergency Operations Center said three mosques, 35 schools and more than 400 homes have been destroyed.
Minister of State Administration, Lucas Chomera, who visited Nampula Sunday, said provincial governments "are able to deal with the situation, and we have instructed them to act quickly."