Six other members of the Turkish crew were rescued after the ship requested assistance several kilometres from the port of Misrata, navy spokesman General Ayoub Qassem said.
He said the Turkish-flagged ship was carrying marble dust and was about 2-2.5 nautical miles from shore when it radioed a call seeking help.
"The search is underway for the seven missing... But the sea is very rough and the waves are high," said Qassem.