Cyclone Kenneth struck with winds of 220km/h (140mph) barely a month after a previous cyclone killed hundreds and devastated large areas.
Heavy rain continued to fall on Friday, raising fears of more floods.
Authorities have advised people to move to higher ground amid concern that thousands may be trapped in remote villages.
Mozambique was still recovering from Cyclone Idai, which killed more than 900 people across three countries in March.
Cyclone Kenneth had already killed three people on the island nation of Comoros. At least one person has been reported dead in Mozambique after being crushed by a falling tree.