Jurgen Klopp’s side were held to a 1-1 draw by Premier League struggles West Brom at Anfield on Sunday.
Sadio Mane gave Liverpool an early lead but the hosts failed to make the most of their dominance before Semi Ajayi headed home a late equaliser.
Matip hobbled off during the Premier League stalemate and looks set to join the likes of Virgil van Dijk and Joe Gomez in the Liverpool treatment room.
With the January transfer window opening next week, Carragher believes it is imperative that his former club strengthen their defensive options as they bid to defend the title.
He told Sky Sports: ‘It’s a massive worry but not a new worry.
‘Joel Matip will not play every game between now and the end of the season you know that even before the injury today and that’s why it’s paramount that Liverpool sign someone in January.
‘I said that as soon as Virgil van Dijk had his injury against Everton.
‘Fabinho’s gone there and looked like a top class centre-back in that position so maybe people at the club felt the need wasn’t as urgent but Joel Matip is just too injury prone.
‘His body just can’t take the rigours of playing in Premier League football week in week out we know that since he joined, he’s a really good player.
‘The only way they don’t win it is if they have problems at centre back where Rhys Williams or Nat Phillips have to play for a prolonged period of time.
‘The odd game coming in now and again they’ve done really well, done fantastic but I know that’s the position I played its not a position for young players as such and at times they will make mistakes as young players, they’re learning.
‘I don’t mean bringing in a centre back for £70m like Van Dijk and not necessarily someone to go straight in the team, just someone there so Liverpool don’t end up maybe with two young lads at some stage in five or six weeks if Fabinho was to go down injured.
‘At this moment Liverpool football have one senior centre-back who’s available this season and he’s injury-prone, so they have to, have to do something in January.’
Liverpool will be hoping to respond to their disappointing draw with West Brom on Wednesday when they face Newcastle United.