The Amiya Scan, managed by the Reider Shipping company, was seized off the coast of northern Somalia on May 25 as it sailed to Romania from the Kenyan port city of Mombasa.
"According to information provided by the ship owner, all crew members are in good health and feeling well," the ministry said in a statement.
Russia earlier urged Somalia not to take any action that could put the lives of the crew in danger.
Somali media reported on Wednesday that the Reider Shipping company paid a $1.25-mln ransom to secure the release of the Amiya Scan and its crew.
Radio Garowe cited Said O'Yusuf, a local mayor in a coastal area near Eyl, as saying that pirates had received the ransom payment in waters not far from Eyl beach.
The waters off the east African nation are considered among the most dangerous in the world. According to the United Nations, 26 pirate attacks on civilian ships have occurred in the area since the start of this year.
On April 4, after a French yacht and its 30 crew were seized by pirates in Somali waters, the French government conducted a military operation, which resulted in the capture of six pirates.
In the beginning of June, the UN Security Council passed a resolution permitting countries to enter Somalia's territorial waters to combat "acts of piracy and armed robbery at sea."
