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Wilson started 27 of the Angels' first 56 games prior to Tuesday night's contest against Seattle, and had only 13 hits and one RBI in 76 at-bats before he was struck in the facemask by a foul tip off the bat of the Mariners' Munenori Kawasaki and was removed from Monday's game.
The Angels now have two catchers on the DL, including Chris Iannetta, who is out with a broken right pinky.
Wilson went on the 15-day DL in April 2010 with a concussion after a bone-jarring collision with the Yankees' Mark Teixeira at home plate -- a play that also resulted in a sprained left ankle.
Conger, who has spent parts of the previous two seasons with the big club, started on Tuesday night.