Mathews' return was a prior arrangement based on "personal grounds", a Sri Lanka Cricket release said, though he had also suffered a hamstring injury during his match-winning 54 not out on Sunday. He is not expected to be available for any of the five-match one-day series.
Pradeep, meanwhile, injured his hand in the opening T20, and Gunathilaka has been laid low by a back complaint. Both are ruled out the rest of the tour. Vice captain Dinesh Chandimal will lead the side in Mathews' stead.
The triple blow is a significant for Sri Lanka's chances in the limited-overs series - all three players have featured in Sri Lanka's ODI sides, and Mathews especially, provides balance to the XI in his all-round role.
The three-wicket win on Sunday was Sri Lanka's first victory of the tour. The third T20 international is scheduled for January 25, and five ODIs are to follow.
The injuries to Gunathilaka and Pradeep may also affect availability for the forthcoming T20 tour of Australia. Sri Lanka are expected to name their ODI squad for the South Africa series on Tuesday or Wednesday.