Sri Lanka were playing their final 50-over warm-up game before meeting South Africa in the opening match of the triangular at Nottingham on Friday.
Jayasuriya was struck by the first ball of the innings by former England bowler Dean Headley which rose off a good length after Kent had won the toss and inserted Sri Lanka first on a fresh pitch. He was treated on the field by physio Alex Kountouri and resumed his innings only to be hit three overs later on the same finger by the other new ball bowler Alan Igglesden.
Jayasuriya was in considerable pain, and that knock on the finger brought Aravinda de Silva, who was leading Sri Lanka in this match and Kent captain Steve Marsh, running onto the ground.
After discussions with the two umpires, it was decided to re-start the match on another pitch used for the league game against Hampshire on Sunday.
Sri Lanka manager Ranjit Fernando said that Jayasuriya suffered the injury on the tip of his left index finger and there was a lot of swelling around it. His hand was kept under ice packs and he was due to go for a precautionary X'ray later in the day.
Only 3.5 overs were bowled on the dangerous pitch, during which period Sri Lanka made 20 without loss, with Jayasuriya scoring five and Kaluvitharana nine before the match was abandoned.
The England and Wales Cricket Board (ECB) chief inspector of pitches Harry Brind was due to arrive here Wednesday and give his opinion on the condemned pitch. The county may face a fine if he gives a bad report on it.