This follows positive swab tests for coronavirus on Friday and Saturday.
Essendon's brief statement on Tuesday said the club would "work with relevant medical experts over the coming days to further understand these results".
McKenna went home for the early stages of lockdown before returning Down Under when an AFL resumption was announced.
Prior to Friday's test, the 24-year-old former Red Hands U21 player had tested negative five times since arriving back in Australia.
