Malinga, 23, missed the six-wicket Super Eights win against New Zealand at Grenada's National Stadium on Thursday after damaging left ankle ligaments during a training session.
With Sri Lanka needing one win from their two remaining Super Eights games to be certain of a semi-final spot, it now looks as if Malinga will miss Monday's match against Australia in a bid to make sure he's fit to face minnows Ireland - who suffered a nine-wicket thrashing Friday by the title-holders - two days later.
"He's been walking and feeling much better," Tissera told reporters Friday. "I don't know whether we will risk him for that game (against Australia).
"He's doubtful. It may be better to keep him for the game against Ireland.
"When he was first diagnosed they said he would be out for a week so we don't know yet."
Malinga, whose distinctive, slingy action makes him hard for batsmen to face has made a major impact upon world cricket during the past year.
At the World Cup he has so far taken 15 wickets in six matches at an average of 14.26.
Only Australia's Glenn McGrath, who has played one game more, is ahead of him in the tournament standings with 18 wickets at 13.05 each while Malinga's Sri Lanka team-mate Muttiah Muralitharan also has 15 wickets, at 17.13.
Despite Malinga's absence, his side enjoyed a comfortable win against title rivals New Zealand.
Left-arm quick Chaminda Vaas (three for 33) and Muralitharan (three for 32), two of the stars of Sri Lanka's 1996 World Cup-winning team, did the damage with the ball in a game their team won with 29 balls to spare.