Iranian media reports the Hankuk Chemi ship was carrying nationals of South Korea, Indonesia, Vietnam and Myanmar.
South Korea's foreign ministry says it has sent a warship to protect other ships in the area, calling for the immediate release of the tanker.
It comes amid tensions between Iran and South Korea, with Iran demanding the Asian nation release $7 billion in funds frozen in its banks due to United States sanctions.
The province's ports and maritime deputy, Ismail Makizadeh, says the tanker is being held at the port city of Bandar Abbas.
