The 31-year-old has played every minute of Swansea's campaign this season and will be leading the Welsh national team at this summer's Euro2016 in France.
Swans boss Francesco Guidolin confirmed in his press conference that he has decided to give a much-needed break to his captain in a bid to freshen him up for Wales' Euro campaign.
"Ash will not play again this season, he needs a break," said Guidolin ahead of Saturday's trip to West Ham United.
"He is tired because he has played a lot of games this season and before.
"Ash is the skipper, a good player and leader, and he is very important for me and our team. But it is better for him to rest and be prepared for the Euros and for next season."