The Sewol sank off Jindo island on 16 April 2014, killing 304 people, almost all of them children.
The bodies of nine people have never been recovered and relatives have long campaigned for them to be found.
The ship was raised in March after almost three years on the sea floor and towed to port.
Workers are searching the silt and debris inside the wreck to search for human remains, while divers are looking on the seabed where the ferry had been lying.
The 34-centimetre bone was found at the site of the sinking.
"The result of a DNA test on a bone piece identified it as Danwon high school teacher Ko Chang-seok," the maritime ministry said in a statement on Wednesday.
The sinking of the Sewol shocked the nation.
Most of those on board were teenagers from the same high school. Many obeyed erroneous crew instructions to remain in their cabins as the ship sank.
The disaster was blamed on a combination of illegal redesigns, cargo overloading, the inexperience of the crew member steering the vessel, and lax government regulations.
The ship's captain was later convicted of murder.
A piece of bone found on the site of the Sewol ferry disaster off South Korea has been confirmed as belonging to one of the missing victims.