The Arctic Sea merchant vessel, recently freed from hijackers by a Russian missile frigate, is being towed by a tugboat to the south Russian port of Novorossiisk, a port official said on Monday.
"We expect the ship to arrive some time in mid or late September," he said.
The Arctic Sea is being escorted by the Ladny missile frigate, which may be later be replaced by another warship.
"This is up to the Navy command to decide," the official said.
Russian Defense Minister Anatoly Serdyukov said on Thursday the Arctic Sea would set out for the Russian Black Sea port for an investigation.
Part of the crew of the Arctic Sea and a group of eight suspected hijackers arrived in Moscow on Thursday on board two military transport planes. On Friday, a Moscow court approved the detention of the suspects.
The Basmanny District Court remanded in custody two Russians, one Estonian and one Latvian, as well as three men with no citizenship, and one whose nationality has not been established.
The men are all unemployed residents of Estonia, where many ethnic Russians have lacked citizenship since the collapse of the Soviet Union. All eight deny accusations of piracy and hostage-taking.
The Maltese-flagged vessel, which had been missing in the Atlantic for more than two weeks, was found off Cape Verde last Monday.