Draper said Thursday his upper-body injury will be evaluated later this week.
He did not play in the first round against the Columbus Blue Jackets.
Draper's plus-minus rating was a team-worst and career-low minus-13 this season for the defending Stanley Cup champions.
Second-seeded Detroit will host the eighth-seeded Ducks on Friday night in Game 1 of the Western Conference semifinals. After Game 2 is played Sunday at Joe Louis Arena, Draper hopes to be cleared to play when the series shifts to California.