The 36-year-old has undergone three operations in the space of 18 months, and that has been enough for him to end his career.
The former Republic of Ireland international told the club's official website: "I am going on 37 and now is the time to bow out. I felt okay in pre-season but my knee just crumbled away.
"Three operations in 18 months basically told me it had had enough. It just wasn't meant to be in the end.
"The fans have been brilliant with me since I came in and I have had a great relationship with them. I will never forget that day lifting the League Cup. It was a big, big thing for me."
Carr made more than 400 appearances during his career, also playing for Tottenham Hotspur and Newcastle United.