Carragher made 221 appearances for the Valiants between 1997 and 2003 and was part of the side that lifted the LDV Vans Trophy at the Millennium Stadium.
The defender, who started his career with Wigan Athletic and also spent two seasons at Macclesfield Town, will be remembered with a minute's applause ahead of Vale's meeting with Chesterfield on Friday.
"We are saddened to hear of the passing of former Vale captain Matt Carragher," a tweet from the official Port Vale account read. "Our thoughts are with his friends and family at this time."
Carragher brought the curtain down on his career in 2005 after making 57 appearances for Macclesfield.