Flexen was recalled from Triple-A Las Vegas on Saturday.
Flexen, who briefly competed for a spot in the Mets' starting rotation in spring training before being assigned to minor-league camp, had a 3.40 ERA and 1.49 WHIP with 31 strikeouts over 39.2 innings for Las Vegas. The 23-year-old is likely to be used as a low-leverage reliever in New York but could also step in as a starter, if necessary.