Helicopters and boats were dispatched to save the 25 staff on board after the Höegh Osaka car carrier that ran aground close to the Isle of Wight at about 9.30pm on Saturday.
Pictures published online showed the 52,000-tonne vessel listing at a 45 degree angle after it reportedly turned sharply to avoid a sandbank as it sailed from Southampton to Germany.
"All of the crew have been accounted for and other than a couple of non life-threatening injuries, everyone is safe and well," National Maritime Operations Centre Commander Steve Carson said in a statement.
Some crew were airlifted off the ship by helicopter and others were rescued from the sea by the three lifeboats that were on scene, the coastguard said.
Three crew who had remained on board the vessel to assist with salvage operations are now also being airlifted off the vessel, it added in a statement on its website.