The Eagles placed Evans on injured reserve Friday and signed corner Bradley Roby from the practice squad to the active roster.
Carter, the No. 9 pick, out of Georgia, hurt an ankle during Wednesday's practice and was sidelined the rest of the week. Coach Nick Sirianni indicated it is not a long-term injury.
The same applies to Slay, who played all of Sunday's game against the Los Angeles Rams but did not practice all week.
Carter leads the team with 3.5 sacks and ranks first among defensive tackles in QB pressures through five weeks with 25, per NFL Next Gen Stats data.
"Man, he's just been playing phenomenal. A young guy with a lot of energy, a lot of juice," said veteran edge player Haason Reddick.
Slay, considered one of the top corners in the league, is second on the Eagles with four passes defended and has one interception on the season.
Defensive tackle Fletcher Cox (back) is slated to return after a one-week absence, which should help offset the loss of Carter.
The Jets are also battling injuries and will be down two of their top four cornerbacks for the second straight week, as starter D.J. Reed (concussion) and dime back Brandin Echols (hamstring) were declared out.
Reed had been trending toward a return after practicing Wednesday and Thursday, but he wasn't able to clear concussion protocols and was held out of Friday's practice. Bryce Hall, who scored last week on a late fumble recovery, will start again for Reed.
Top corner Sauce Gardner also sat out Friday with an illness, but he's expected to play despite being listed as questionable, according to coach Robert Saleh. The Jets also may have to switch punt returners, as rookie Xavier Gipson showed up on the injury report as questionable with an ankle injury. Mecole Hardman, a healthy scratch last week, likely would replace Gipson.
ESPN's Rich Cimini contributed to this report.