"With His Majesty the King, the Queen and the adorable young Prince of Bhutan. Happy to see HM the Prince like the Chennapatna (Karnataka) toys," Sitharaman tweeted.
She also posted photographs of her meeting with the royal family.
The details of the meeting were not immediately available.
The Bhutanese King, accompanied by Queen Jetsun Pema Wangchuck and one-year-old prince Jigme Namgyal Wangchuk arrived here on Tuesday on a four-day visit.
This is the first high-level visit from Bhutan to India after the end of the 73-day-long Dokalam standoff between armies of India and China near the India-China-Bhutan tri- junction.