Power has been cut off and key bridges flooded on the Manicaland province which borders Mozambique.
Some passengers said, though, that they were unaware of the cancellations until they arrived at the airport attempting to leave.
Home Affairs Deputy Minister, Cde Mike Madiro said rescue operations continue in search of the over 70 people who remain missing.
"The information we have so far is that over 100 people are missing", said Joshua Sacco, an MP in Chimanimani district.
"At least 25 houses were swept away following a mudslide at Ngangu township in Chimanimani urban. There were people inside", he told AFP, saying they were listed as missing. The country's national army was leading the rescue efforts, it added.
With heavy rain and winds of up to 170 kilometers per hour (105 mph), Tropical Cyclone Idai unleashed widespread damage and destruction Friday on the port city of Beira, leaving more than a dozen dead and cutting off communications and electricity.
Zimbabwe's opposition Movement for Democratic Change spokesman Jacob Mafume tweeted that a "serious humanitarian crisis (is) unfolding" in eastern Zimbabwe districts.
The United Nations said more than 100 people had already died in weeks of heavy rain and flooding in Mozambique and Malawi.
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In February 2000, Cyclone Eline hit Mozambique when it was already devastated by its worst floods in three decades.
"We need state intervention on a massive scale to avoid biblical disaster", he said.
Heavy downpours in neighbouring Malawi this week have affected nearly a million people and claimed 56 lives there, according to the latest government toll.
As the cyclone approached, the Red Cross sent out more than 200 volunteers to areas most likely to be affected.
As per reports, the city's power grid has crashed, airport shut and roads inundated.
Describing it as a "difficult emergency" to tackle, he told AFP said it would require "the full force of the humanitarian community behind the government of Mozambique to respond to rapidly".
When the cyclone hit Mozambique, authorities there were forced to close the worldwide airport in the port city of Beira after the air traffic control tower, the navigation systems and the runways were damaged by the storm.
The cyclone is expected to also affect Mashonaland East, Mashonaland Central and Masvingo provinces, with the later having already witnessed the effects of the deadly storm after Mutimurefu Prison's four cells had roofs blown away this morning. It killed 350 people and made 650,000 homeless across southern Africa.
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