Australian batsman Aaron Finch has led the side in a lot of games as Mathews was dropped due to poor form.
"It is in our best interests that the captaincy is not switched frequently as we strive to achieve the best balanced team for each different opponent. Given that Aaron (Finch) is likely to play in all our remaining games then it is logical that he continues to be our captain," Mathews said in a statement.
The Sri Lankan said he would continue to be a member of the side.
"I will naturally provide my fullest support at all times to Aaron and my team-mates. I will also continue to work as hard as possible as a player as we all strive to win our remaining matches," he said.
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