The tournament begins Monday.
Keys, an American who was seeded 19th at the All England Club, pulled out because of a hurt abdominal muscle.
She was replaced in the field by Coco Vandeweghe, twice a quarterfinalist at Wimbledon and twice a semifinalist at other Grand Slam tournaments, who lost in qualifying this week. Vandeweghe's first-round opponent will be No. 17 seed Elena Rybakina.
Coric is a Croatian who got into the field thanks to a protected ranking because he has been injured. He cited a shoulder problem for his withdrawal.
He was drawn to face No. 12 seed Diego Schwartzman and that spot will be filled by an as-yet-unannounced player who lost in qualifying.