The Nigerian pulled up in the first half at Selhurst Park, and was replaced by Davide Zappacosta in the 40th minute.
Into the last couple of minutes of the half, it remains 1-1 and Zappacosta has replaced the injured Moses for Chelsea. #CRYCHE— Chelsea FC (@ChelseaFC) October 14, 2017
Moses has started six of Chelea's eight Premier League matches this term, after becoming a fixture in the Blues line-up during their title-winning campaign last season.
Palace went on to win Saturday's game by a 2-1 score, after netting their first two league goals of the season.
Following the defeat, Chelsea boss Antonio Conte lamented the club's worsening injury situation.
“I think, in this moment, for us it's a very difficult moment," Conte said.
"When you start a game without Morata and without Kante, it's not simple.
"Above all if, during the game, another important player in your team has an injury too like Victor Moses. I hope to have him back very soon because this moment is very difficult for us.
"To lose three or four players ... it's a big problem for us. But, despite this, we have to find the will to fight. I think this season will be very difficult and, for this reason, we have to put 150 per cent in.
"It's not enough to put 100 per cent in like last season. I think this season, me first, the staff and the players have to put in 150 per cent because the season will be very difficult."