Castillo reportedly suffered the injury earlier this month when he was jammed on a pitch.
In August, Castillo, 27, signed a deal reportedly worth $72 million over seven years with the Red Sox.
In 40 plate appearances over 10 games this season, Castillo posted a .333 batting average with two home runs and six RBI.
Castillo was reportedly expected to play in Puerto Rico this winter.
The Red Sox went 71-91 last season and finished in last place in the American League East.