Right-handed reliever Liam Hendriks will be on the mound for the start of Wednesday night's game, and A's manager Bob Melvin would not say who will follow.
His bullpen includes just one left-hander, Ryan Buchter. The righties in addition to Jackson are closer Blake Treinen, Lou Trivino, Jeurys Familia, Shawn Kelley, Emilio Pagan, Yusmeiro Petit, Fernando Rodney and J.B. Wendelken.
Mike Fiers, among Oakland's few healthy starting pitchers, was left off the roster for Wednesday's game. If the A's advance, he would be in position to start an AL Division Series opener at Boston on Friday.
Fiers, who made his first relief appearance of the season on Friday against the Los Angeles Angels, replaced Trivino in the second and allowed six runs in 3 1/3 innings.
Teams may change rosters after each round.