The ministry said in a statement it would hold a briefing on “finding human remains suspected to be one of the missing victims”.
The wreck was brought to the surface last week, nearly three years after it went down killing more than 300 people, and placed onto a semi-submersible ship that will finally bring it to shore.
Almost all the victims were schoolchildren and nine bodies were still unaccounted for, raising the prospect that they could be trapped inside the vessel.
The remains were recovered on board the semi-submersible carrying the ferry, Yonhap news agency said, without immediately giving further details or citing a source.
Yonhap said officials from the National Forensic Service as well as ministry officials and police have been dispatched to the site to identify the remains.
The 145-metre ship was brought to the surface in a complex salvage operation believed to be among the largest recoveries ever of a wreck in one piece.
Doing so had been a key demand of the families of the nine missing victims — four schoolchildren, two teachers, and a married couple and their child who were moving to Jeju, the ship’s destination, to set up a new life.
Divers wrapped up their search in November 2014, and since then a handful of relatives set up home at Paengmok, a port an hour away from the accident site.
The semi-submersible is expected to set off for Mokpo, a large port on the southern coast some 87 kilometres (54 miles) away, on Thursday.
As part of the salvage operation, underwater fences were set up around the wreck and searches will be carried out in the area as well as on board the Sewol.
The salvage came as the third anniversary approached of one of the country’s worst-ever maritime disasters, which dealt a crushing blow to now-ousted president Park Geun-Hye.
Investigations concluded the disaster was largely man-made — the cumulative result of an illegal redesign, an overloaded cargo bay, inexperienced crew and a questionable relationship between the ship operators and state regulators.