The EMS Majestic, which is registered in Antigua and Barbuda, issued a Mayday call from its position in the Dover Strait just after 19:00 GMT on Sunday.
A number of ships in the area responded to the sinking vessel, according to the Maritime and Coastguard Agency.
Two of the ship's crew of seven were airlifted to land for safety reasons.
Coastguard helicopter crews from Lee-on-Solent, Hampshire, and Lydd, Kent, were scrambled for the rescue, along with the RNLI lifeboat from Eastbourne, East Sussex.
The EMS Majestic was being towed to a safe haven by the tug Thor Frigg.
The cargo of the 90m-long ship has not been disclosed.

Parking controls will be implemented between 12:30 and 18:00 in zones 1-4.
Councillors said this would reduce traffic "chaos" on some streets and encourage more people to use buses, trams or bicycles to get into the city.
But they heard warnings that the restrictions could affect footfall in the city centre and faith groups which meet on Sundays.
Conservative councillor Nick Cook warned that the parking charges could affect church congregations.
He said he feared that the charges set a "dangerous precedent" and could be extended in the future.
"It will be bad for society, bad for business and bad for Edinburgh," he said.
However, Nigel Bagshaw, of the Scottish Green Group, urged the transport and environment committee to implement all-day parking charges.
He said the move would improve health, safety, air pollution and emissions.
"We have to make bold choices," he added.
SNP councillor Gavin Barrie backed the limited parking charges, claiming they would make the city centre more accessible to the vulnerable.
He said people in wheelchairs and those pushing prams struggle to get around when vehicles were badly parked.
Councillor Lesley Hinds, the convenor of the committee, said the restrictions were appropriate for a "seven-day city".
She added: "Not only will this make parking easier for residents and visitors by increasing parking turnover, but we hope, in turn, it will encourage more people to choose public transport or active travel over the car by creating safer, more free-flowing roads.
"Therefore I believe that we've agreed the best option for Edinburgh. By introducing restrictions on Sunday afternoons we want to strike a balance for all those that live in and visit the city, and I think that our final decision reflects the fact we really listened to the concerns of various groups and individuals."
The motion to introduce parking charges on Sunday afternoons was approved 10 votes to two.
It is expected to be implemented around the end of 2018.
A cargo ship is being towed to port after it began taking on water and sinking while under way in the English Channel, the coastguard has said.
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Councillors in Edinburgh have agreed to begin charging drivers to park in the city centre on Sundays.