The vessel was shelled from the coast on Sunday while approaching the port of Tobruk. When it tried to leave the dangerous area, it was attacked from the air.
Istanbul condemned the assault which took place in international waters but did not name the attackers.
"We strongly condemn this cowardly attack carried out against a civilian ship in international waters, we condemn those who carried out the attack", the Ministry's statement read.
Libya has been mired in political turmoil since the overthrow of its longstanding dictator Muammar Gaddafi in 2011, with the country’s internationally recognized government fighting against rival Islamist-backed authorities and numerous militias.
In February, Libya’s Prime Minister Abdullah al-Thinni, from the internationally recognized government, in a televised interview accused Turkey of delivering arms to the rival government group.