The mayor of Beira in the country's province of Sofala, Davis Simango described the scenario as "the most dramatic ever to be seen in the country´s recorded history".
The official urged residents in the city to leave risky areas and avoid death.
"Priority now is to save lives since there is nothing we can do to avoid destruction of infrastracture because we had not anticipated how violent the storm could be", Simango told private television Stv in Beira late on Thursday without revealing any death.
He added: "the wind is between 200 and 220 kilometres per hour and roads have been turned into rivers".
President Filipe Nyusi of Mozambique appealed for people in risky areas to heed the call to evacuate without taking along their belongings.
"This is a more dangerous situation for people to think that the rain and the wind will subside soon, we have rescue people on the ground and we are appealing to those in risky areas to leave before it gets worse", he warned on state television on Thursday night.
The meteorology department said the cyclone will dump heavy rain and wind over Mozambique, before moving to southern Malawi and later Zimbabwe
The government's National Institute for Disaster Management (INGC) says that 66 people have been killed and 141,000 others were affected after heavy rains pounded the country's central and northern regions.
It has appealed for funds to manage the crisis.
Home to some 28.8 million people, Mozambique suffers from periodic cyclones, droughts, floods, and related natural disasters.
Since storms began more than a week ago, around 83,000 people have been displaced after rivers burst their banks, leaving villages underwater and knocking out power and water supply infrastructure in some areas.