Egbert, whose contract was selected from Triple-A Buffalo of the International League, was to be in uniform for Friday night's game against the San Diego Padres. The 29-year-old was 2-3 with a 2.08 ERA in one start and 16 relief appearances with the Bisons.
Carson allowed two runs in three innings over two games with the Mets.
New York also released D.J. Carrasco, who was designated for assignment May 16 after allowing a home run to Todd Frazier with his first pitch in a 6-3 loss to Cincinnati. The 35-year-old right-hander had a 7.36 ERA in four appearances.
The Mets are responsible for the remainder of his $1.2 million salary.