Acting Interior Minister Bruno Retailleau said the storm had left a "dramatic" trail of destruction on the impoverished islands, warning that the territory's numerous shantytowns had been "completely destroyed".
"It will take several days" to establish the death toll, but "we fear that it is heavy", he said as he left a government crisis meeting chaired by France's newly appointed Prime Minister Francois Bayrou.
Retailleau will travel to Mayotte on Monday, his office said.
The cyclone had put the region on high alert as it closed in on the African mainland, packing gusts of at least 226 kilometres (140 miles) per hour.
The storm also hit the nearby Comoros islands, causing flooding and damaging homes.
The two confirmed deaths came on Petite-Terre, the smaller of Mayotte's two major islands, a security source told AFP.
Acting Transport Minister Francois Durovray said on X that Petite-Terre's Pamandzi airport had "suffered major damage".
Health Minister Genevieve Darrieussecq said the entire territory's health system had been "severely affected", with "major material damage to the Mayotte hospital centre".
Earlier Saturday, Defence Minister Sebastien Lecornu said an A400M transport plane would be leaving France carrying aid and "civil security" equipment.
Retailleau's office said he had spoken by phone to the prefect for the territory, ordering "full mobilisation" of police and security services to help residents and "prevent any possible looting".
- Headed for Mozambique -
Just northwest of Mayotte, the Comoros islands, some of which had been on red alert since Friday, were also hit, though less hard than the neighbouring archipelago, said national civil security chief Abderemane Mahmoud.
The storm flooded mosques, swept away boats and damaged homes on the islands of Anjouan and Moheli.
Comoros President Azali Assoumani had appealed to citizens in an address to "heed the authorities' instructions better than in 2019", when Cyclone Kenneth devastated the islands.
"Our country is in a high-risk zone, but we must learn to manage these storms," he said.
Chido is expected to make landfall early Sunday in northern Mozambique's Cabo Delgado or Nampula provinces.
Cyclone Chido is the latest in a string of storms worldwide to be fuelled by climate change, according to experts.
The "exceptional" cyclone was super-charged by particularly warm Indian Ocean waters, meteorologist Francois Gourand of France's Meteo France weather service told AFP.
The United Nations Office for the Coordination of Humanitarian Affairs (OCHA) said Friday it was similar in strength to cyclones Gombe in 2022 and Freddy in 2023, which killed more than 60 people and at least 86 in Mozambique respectively.
It warned that some 1.7 million people were in danger, and said the remnants of the cyclone could also dump "significant rainfall" on neighbouring Malawi through Monday, potentially triggering flash floods.
Zimbabwe and Zambia were also expected to see heavy rains, it added.
- 'Lost everything' -
Mayotte, which sits 500 kilometres east of Mozambique, is France's poorest department.
"Many of us have lost everything," said prefect Francois-Xavier Bieuville, calling Chido "the most violent and destructive cyclone we've seen since 1934".
Mayotte's alert level had been lowered from violet -- the highest -- to red to allow emergency responders to leave their bases.
But "the cyclone is not over", Bieuville warned, urging Mayotte's roughly 320,000 people to remain "locked down".
Communications with Mayotte are largely cut off.
Earlier, a resident on the main island of Grande-Terre, Ibrahim Mcolo, described fallen electricity masts, roofs ripped off homes and trees uprooted as the first gusts struck.
"There is no more electricity," he told AFP from his home, where he had barricaded himself in.
"Even in our house, which is well protected, the water is getting in. I can feel it trembling."
"It is a time of emergency," President Emmanuel Macron wrote on X, telling Mayotte residents that "the whole country is by your side" and thanking emergency responders.
Retailleau announced that 140 fresh troops and firefighters would be sent to the scene on Sunday to help with recovery, more than doubling the deployment sent earlier in the week.
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