The former Ajax man opened the scoring on the night before landing awkwardly on his shoulder at the end of the first half, ultimately being replaced by Christian Pulisic.
Ziyech returned for the trophy presentations with his arm in a sling, and Chelsea boss Thomas Tuchel has not been able to offer a positive update on the 28-year-old's condition.
Speaking to reporters following his side's penalty shootout win over the Yellow Submarine, Tuchel said: "If you take a player out during the first half it's serious.
"We overused some players who were absolutely not ready to play 120 minutes and have only two days in between this and the next match with Crystal Palace so that absolutely does not help us."
Ziyech continues to be linked with a move away from the Blues, though, with AC Milan rumoured to be interested in the Moroccan attacker, who claimed six goals and four assists from 39 games last term.