The incident, which Sydsvenskan was the first to report, occurred on Saturday. The vessel remained on Sunday, off Klagshamn in southern Malmö.
Then, a Danish military vessel was near the Russian vessel, and a British-flagged Nato vessel also approached the location.
The Danish Navy confirmed the information to Danish TV2, but did not want to release more information.
The Swedish Coast Guard's control center told TT that the vessel, Mechanic Stepanov, had suffered a total power failure.
During Sunday afternoon, Mechanic Stepanov was able to start moving again.
Now the fishing vessel has just weighed anchor and is on its way out. The problem was supposed to be a "black-out", some kind of power problem, says Pontus Ekström, duty officer at the Coast Guard, to Sydsvenskan.