Gibson, speaking before Sunday's game against Cincinnati, said that timetable was just a guess.
The Diamondbacks put Pollock on the 15-day disabled list and purchased the contract of outfielder David Peralta from double-A Mobile (Ala.). Peralta was in the Arizona lineup in left field for Sunday's game, his major league debut.
He had been one of the team's best players over the last month, batting .344 since April 4.
Vogt immediately went into the starting lineup at catcher for the series finale against the Angels as the short-handed A's needed hitters with first baseman Brandon Moss (right calf) and outfielder Josh Reddick (knee) out because of injuries. Both are day to day.
Infielder Nick Punto is also slowed by a sore calf, leaving Oakland with only 10 healthy hitters before the move to bring up Vogt.
Myers was injured on the final play of a 3-2 loss Friday to the Boston Red Sox when his hand slapped the ground as he landed following a collision with center fielder Desmond Jennings. The collision led to a game-ending triple by A.J. Pierzynski in the 10th inning.
Myers, who also sat out Saturday's game, is batting .227 with five home runs and 25 runs batted in this season.