The Board of Control for Cricket in India said left-handed batter Sudharsan had made "significant progress" in recovering from a toe problem, but that Khan would replace him.
The opening Test will begin on August 15th in Galle. The second Test will be played between August 23rd-27th in Colombo.
The series will be India's first in the current World Test Championship (WTC) since the 2-0 home defeat to South Africa in November.
India are fifth in the WTC standings, which are led by Australia, with Sri Lanka sixth.