Rizwan and Irfan both suffered hamstring injuries in the third match in Rawalpindi, where a second-string New Zealand side won by seven wickets to level the five-match series 1-1
Sri Lanka Cricket said the 35-year-old fast bowler would depart after the match against Bangladesh in Bristol to attend the funeral of Kanthi Perera in Colombo on Thursday.
"He is expected to join the team before the next World Cup game, which will be played against Australia on 15th," SLC said in a statement.
Malinga has had a mixed World Cup so far.
He had a match to forget in the opening 10-wicket defeat by New Zealand when he conceded 46 runs in five overs without taking a wicket but bounced back with 3-39 in the 34-run victory over Afghanistan.