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.
Mumbai Indians's IPL campaign came to a disappointing end on Sunday when they were eliminated from the playoff race following a two-wicket defeat to Royal Challengers Bengaluru in Raipur.
Royal Challengers Bengaluru beat the Mumbai Indians in dramatic fashion to go top of the Indian Premier League, with the Chennai Super Kings chasing a huge total against the Lucknow Super Giants in the other match on Sunday.
Afghanistan mystery spinner Rashid Khan admitted that he underperformed due to his impatience with his recovery after back surgery.
Shubman Gill played a captain's knock with the bat while Rashid Khan shone with the ball to help Gujarat Titans beat Rajasthan Royals by 77 runs in their IPL clash.
