Carse, who has not played in Sunrisers' first five fixtures in 2026, hurt his right hand while batting in the nets and has not recovered.
Madushanka, who has played one Test, 28 ODIs and 19 T20Is for Sri Lanka, has not yet played in the IPL but was part of the Mumbai Indians squad in 2024.
Sunrisers are already missing regular captain and premier fast bowler Pat Cummins as he recovers from a back injury.
It has resulted in two rookie seamers, Praful Hinge and Sakib Hussain, making impressive debuts in Monday's victory against Rajasthan Royals.
Sunrisers have two wins and three defeats in five games so far this season and next take on Chennai Super Kings on Saturday.
In a classic Wankhede run-fest on Thursday night, Punjab Kings produced a clinical chase to dismantle Mumbai Indians by seven wickets with 21 balls to spare in IPL 2026's 24th match.
Australia quick Pat Cummins is finally set to run out for Sunrisers Hyderabad in the Indian Premier League on 25 April.
Royal Challengers Bangalore secured their fourth victory of the Indian Premier League season after beating Lucknow Super Giants by five wickets at the M Chinnaswamy Stadium.
Chennai Super Kings condemned Kolkata Knight Rider to a fifth straight defeat in this season's Indian Premier League after a 32-run victory at the MA Chidambaram Stadium.
