England yongster Brewster, 17, was subbed off before half time of the reserves game.
Medical staff attended the Reds academy product, who is said to have been clearly in pain.
He was replaced by Reds striker Liam Miller.
Brewster was not the only player to go off in the U23s clash.
The incident happened in stoppage time in the first half after City’s Benjamin Garre was also withdrawn with an injury.
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City won the game 3-2.
Brewster is yet to make a first-team appearance for Liverpool but is tipped as one of their stars for the future.
He was a key member of the England team that won the U17 World Cup last summer.
Liverpool boss Jurgen Klopp talked up Brewster’s future last summer, saying: “Rhian is very similar as a person to Ben Woodburn.
“He never thinks about what team he’s playing for. Ready to make difficult steps.
“These boys are the future and we need to build the present.”
Argentine Garre, meanwhile, joined City last summer.
He scored in their Football League Trophy clash with Rotherham back in August.