The Celtic full-back is the third player to pull out of Chris Coleman's squad for their first Euro 2016 qualifier against Andorra next week.
Matthews – who joined Hal Robson-Kanu and James Collins in withdrawing – has been replaced by Cardiff City's Declan John.
Gareth Bale and Aaron Ramsey headlined Wales' 23-man squad for the match as they begin their bid to qualify for a first major tournament since 1958.
New Leicester City signing Tom Lawrence is one of four uncapped players included in the squad, joining goalkeepers Owain Fon Williams and Kyle Letheren, and midfielder Jake Taylor.
Doubts still persist over whether Andorra will be able to host the match due to the condition of their newly laid 3G artificial pitch.
The surface failed tests on Thursday that indicated the ball was rolling too fast and the match may be moved to another country as a result.