The £4.7million summer signing from Mainz was injured in Wednesday's defeat to Chelsea in Pasadena, and Press Association Sport understands he will fly home on Friday and is likely to require surgery.
Karius was brought in as competition for established number one Simon Mignolet and there was a realistic chance he would have started the Reds' opening match at Arsenal on August 14.
The German had a scan on Thursday after complaining of some discomfort, and his worst fears have been confirmed.
Karius turned down a place in Germany's Olympic squad in order to fight for a starting place at his new club.
Fellow new signing Alex Manninger, a veteran signed from Augsburg on a free transfer, will now deputise for Mignolet for the start of the campaign.
Source: PA