Los Angeles also announced defenceman Keaton Ellerby was claimed off waivers by Winnipeg.
Carter has five goals and four assists in 14 games this season, tying with Justin Williams for the team lead in goals. The forward led the Western Conference with 26 goals last season.
The Kings haven't specified the nature of Carter's injury, but he was wearing a walking boot Friday at practice.
Ellerby still hadn't played for the Kings this season. Los Angeles acquired him from Florida for a draft pick in February.