Grujic clashed heads with Blues winger Bertrand Traore in Thursday morning’s 1-0 defeat at the Rose Bowl, and was substituted at half-time as a result.
After treatment at Huntington Memorial Hospital, the 20-year-old was diagnosed with having suffered concussion, as reported by the Liverpool Echo.
With Liverpool advised to take precaution with the young midfielder, Grujic will be unavailable for Sunday morning’s clash with Milan.
However, it is believed there will be no long-standing effects for the Serbian, who could return against AS Roma on August 2.
Liverpool were without Joel Matip, Joe Gomez, Nathaniel Clyne and Lucas Leiva on Thursday due to injury, with Emre Can, Georginio Wijnaldum, Simon Mignolet, Divock Origi, Daniel Sturridge and Christian Benteke also out while they build fitness.
Clyne could return to action against Milan, filling a problem position at right-back, while the latter group are also expected to be available.
Grujic’s concussion is a blow to both player and manager, with the former Red Star Belgrade youth impressing in his appearances for the Reds so far in pre-season.
Strong, agile and with an eye for goal, Grujic looks set to shine in a box-to-box role in midfield.
After their clashes with Milan and Roma, the Reds will return to the UK for a showpiece ICC fixture against Barcelona at Wembley Stadium (August 6).