The affected destinations are said to include Chennai, Cochin and Bangalore.
A pilots' union official said efforts were being made to bring operations back to normal as soon as possible.
"There was no industrial action as such, but when some pilots report sick operations are disrupted because we are short staffed," a senior union official told LBO.
The union had put forward proposals to the government which they were expecting the government to resolve.
SriLankan Airlines was managed by Emirates up to March 2008, when the Dubai-based airline which owns 43 percent of the Sri Lankan carrier terminated deal after relations with the government soured.
About 35 pilots had left the airline in recent weeks. Emirates also lifted a hiring ban on Sri Lankan Airlines pilots after it terminated the management contract.
The airli