Manager Don Mattingly said the players have been informed of their roles, but the roster won't be announced until it is submitted to MLB on Friday.
However, veteran reliever Jim Johnson was sent home.
Van Slyke, who first injured the wrist Sept. 15, returned five days later but reinjured the wrist when brushed by baserunner Marlon Byrd while taking a throw at first base last week.
A cortisone injection did not relieve the inflammation. Van Slyke said he was able to throw but not hit.
While Puig was out of the lineup in September with a strained hamstring, newly acquired Justin Ruggiano took his place and was productive as a right-handed-hitting outfielder.