Carragher's injuries will not require further treatment, but the diagnosis would appear to rule him out of Tuesday's Champions League third qualifying round second leg against Toulouse.
There is better news over fellow centre-back Sami Hyypia, who was also forced off on Saturday with what has been confirmed as a broken nose.
He is expected to be able to play against the French club, however, after coming through a training session at Melwood on Sunday.
A Liverpool spokesman told the club's website: "Sami has a broken nose but will be available for the second leg of our Champions League qualifier.
"Jamie underwent a series of investigations on Sunday morning which confirmed he has a broken rib and has also developed a pneumothorax.
"He will continue to be monitored on Sunday but at this stage no further treatment will be required."