Jakarta said at the time that its coast guard had seized the MT Horse vessel over the suspected illegal transfer of oil in the country's waters.
However, the Iranian foreign ministry said the seizure was over "a technical issue and it happens in shipping field."
"The MT Horse, belonging to the National Iranian Tanker Company that had been detained in Indonesian waters since January 24, was released on Friday,” state broadcaster Seda va Sima said.
“This vessel has now resumed its mission before returning to the country’s waters,” it added without giving further details.
The Indonesian coast guard said they were checking the Iranian report.
Iran, which is under harsh US sanctions that mainly target its oil exports, has been accused of concealing the destination of its oil sales by disabling tracking systems on its tankers. Last year, it used the MT Horse to deliver 2.1 million barrels of condensate to fellow US-sanctioned Venezuela.