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.
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.