This photo shows stranded workers from a barge being airlifted by naval personnel in the Arabian sea. AFP

Eighty-nine people remained missing in India and hundreds of thousands were without power on Wednesday in the wake of a major cyclone, adding to the country's woes as it suffered a record number of Covid-19 deaths.

Driving waves of up to 25 feet on the high seas, cyclone Tauktae rammed into the western states of Maharashtra and Gujarat over the past two days, killing at least 29 people and leaving a trail of destruction, authorities said.

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The storm smashed into the Bombay High oilfield near Mumbai, where India's biggest offshore oil rigs are located, and sank the barge that had 261 personnel on board.

The defence ministry said Wednesday that Navy ships had rescued more than 600 people after waves up to eight metres (26 feet) high hammered offshore oil installations, according to Agence France-Presse.

A damaged portion of a building is pictured after heavy winds caused by Cyclone Tauktae in Mumbai. Reuters

But planes and helicopters were still searching for 89 workers missing from one of several support vessels that slipped its moorings in the storm and sank.

The navy said 184 people had been rescued from the barge "P305", which was engaged in contract work awarded by Oil and Natural Gas Corp, India's top exploration company.

Three ships and aircraft are continuing to look for the remaining personnel, it added.

More than 16,500 houses were damaged, 40,000 trees were uprooted and nearly 6,000 villages were without electricity.

Power was restored to around 2,100 villages, but hundreds of thousands of people remained without power on Wednesday.

A damaged vehicle is seen under a fallen tree on a road after heavy winds caused by Cyclone Tauktae in Mumbai. Reuters

Prime Minister Narendra Modi is scheduled to conduct an aerial survey later in the day of the storm-hit areas in his home state Gujarat, where the cyclone made landfall on Monday packing gusts of up to 210 kph (130 mph), the state government said.

The storm has piled pressure on Indian authorities as they grapple with a massive rise in coronavirus infections and deaths as well as a shortage of beds and oxygen in hospitals.

In Gujarat, among the hardest hit states by the second wave of the virus, the cyclone has ripped out power pylons, damaged some 16,500 homes and blocked over 600 roads, authorities said.

The state's farm sector is also likely to have taken a hit, including the major mango growing belt of Saurashtra.

Officials said work to restore electricity supply and clear roads was ongoing, but some parts were still cut off.

"Mobile phone networks are still down in many areas, and I don't think they will be restored by today," Aayush Oak, the top official in Gujarat's Amreli district, told Reuters.