Speaking to TV Guide, series showrunner Andrew Schneider said, "It happens in the first half of the season," which probably doesn't instill a lot of positive feelings in fans.
Additionally, Schneider isn't revealing who the character exiting will be, other than to suggest to the outlet that it's someone significant.
Research into what many of the actors have going on career-wise other than Chicago Med didn't reveal anything concerning that would pull any of the main cast away, but there is a potential clue for one of the reccurring actors.
That doesn't necessarily mean she will be the one exiting, but it can be difficult to balance multiple series, so it's plausible that Cox may choose one over the other, effectively leaving open the option to simply allow the character to fully exit.
While at this time there is only speculation as to who might leave Chicago Med, Schneider did reveal that near the end of the current season they will "very likely will have a new character introduced..."
Chicago Med recently came back from their brief winter break and has resumed airing Tuesdays on NBC.