Andujar hurt a shoulder last year and lost the third-base job to Gio Urshela, then returned from surgery and hit .242 with one homer and five RBIs in 62 at-bats. He last played Sept. 13 and was optioned to the alternate training site two days later.
He batted .297 in 2018 with 27 homers and 92 RBIs.
Montgomery is not expected to start against the Indians and will be a bullpen option, likely as a long reliever. New York's rotation includes Gerrit Cole, Masahiro Tanaka and either J.A. Happ or rookie Deivi Garcia.
Ford is a left-handed option off the bench for the heavily right-handed Yankees lineup and a backup at first to Luke Voit, who has played through a foot injury,
Yankees manager Aaron Boone said left-hander James Paxton could be a possibility later in the postseason. Paxton has not pitched in a game since Aug. 20 because of a strained flexor tendon in his pitching arm and was transferred to the 45-day injured list Sept. 16.