Sports Minister Dayasiri Jayasekera said a suspected bookmaker had approached two Sri Lankan players ahead of the match to try to convince them to under-perform and lose the match.
Both players turned down the approach and the authorities were informed, Mr Jayasekara said.
Sri Lanka went on to win the game.
Wicketkeeper Kusal Perera and bowler Rangana Herath were approached shortly before the match in Galle, Sri Lanka, in October, the minister said.
"After Kusal turned down the offer, the man approached Herath who also rejected the offer and alerted the authorities," he added.
Both a police inquiry and anti-corruption investigation by Sri Lanka Cricket have been launched.
The International Cricket Council has also been informed.
Sri Lankan authorities are investigating an attempt to fix an international cricket match involving the national team and the West Indies.