Carragher suffered the blow in the 2-1 defeat at Tottenham at White Hart Lane on Sunday.
Hodgson told Sky Sports: “It’s very bad. He’s dislocated his shoulder.
“It’s an unfortunate thing to happen on his 450th appearance in the Premier League.
“He’s a very important player for us. We’ll now be without him and Steven Gerrard and they are the lifeblood of our club.”
