Bairstow's unbeaten 108 off 48 balls, with eight fours and nine sixes, see Punjab secure the win with eight balls to spare
Chandimal sustained the injury when he was caught on the hand by a Hardik Pandya bouncer in Sunday's match at the Pallekele International Cricket Stadium, which India won by six wickets to take an unassailable 3-0 lead in the series.
"SLC confirms that test captain Dinesh Chandimal will be out of action for the rest of the series after sustaining a hairline fracture to his right thumb," Sri Lanka Cricket said in a statement.
"We will have a better idea of timeline of his recovery after consulting a specialist in Colombo tomorrow."
The teams move to Colombo for the fourth one-dayer on Thursday with the fifth to follow in the capital on Sunday. They will also face off in a Twenty20 international on Sept 6.