The 37-year-old chess player from Perm scored 12.5 points at the end of the tournament.
The gold medal was won by 17-year-old Bibisara Assaubayeva (14 points) from Kazakhstan.
The third place was taken by the Russian woman Valentina Gunina (12 points).
As a reminder, on December 28, Kosteniuk won the world rapid chess championship in the rapid discipline for the first time.
Earlier, Ian Nepomniachtchi spoke about his defeat in rapid at the World Rapid Chess Championship.