McKenna, who returned from his native Ireland last month, was due to feature for the Bombers in their round three clash at the MCG on Sunday.
The blow to AFL fans comes as a spike in Victoria’s coronavirus infections has seen Premier Daniel Andrews tighten restrictions that were set to be eased on Monday.
AFL chief executive Gillon McLachlan confirmed the match was postponed at a press conference at the MCG on Saturday.
“Essendon player Conor McKenna returned a low-grade irregularity yesterday after being tested as part of our COVID-19 protocols,” McLachlan said.
“He was tested again today and we were informed this afternoon that the test came back (positive).
“The health department has been notified as per the protocols and we will be working with (them) to identify close contacts and isolate them.
“At the moment all players and football department staff have been told to isolate until that work is done.”
McLachlan revealed McKenna had been tested five times while in hotel quarantine on his return from Ireland and had returned negative results each time.
McKenna was kept away from a training session on Saturday morning after returning the irregularity on Friday.
“He was tested on Wednesday and was negative and there was such a low level in his test on Friday that it came up as an irregularity,” McLachlan said.
“And then it was a positive test (on Saturday) morning.
“So based on those facts, he’s picked it up this week here in Australia. But again, I will defer to the health department.
“They are the facts as we know them.”
It remains unclear when the Melbourne game will be played or even if Essendon will be allowed to play their round-four clash against Carlton at the MCG.
“I don’t have an answer (yet) but what I do know is we have time and flexibility,” McLachlan replied, when asked about rescheduling the match.
“Whether we compress the season or whether there ends up being a bye …
“It’s why we’ve got this rolling four-week fixture and shorter quarters, so we’ve got the flexibility to deal with this.”
Re-shuffled start times
Starting times for Sunday’s other matches, both at Metricon Stadium, were moved following the postponement.
Gold Coast and Adelaide’s clash will move from 1:05pm (AEST) to 3:05pm, while Fremantle and Port Adelaide’s match starts at 8.10pm, two hours later than originally scheduled.
“We said at the outset of this crisis that we would make all decisions based on medical advice and our priority remains the health and safety of our players, staff and the wider community,” McLachlan continued.
“That is priority one, priority two and priority three.
“We need to do the right thing and the right thing for our club and the wider community is to postpone this match.
“Other matches will proceed.
“All Essendon players and staff were tested last night and Conor McKenna was the only one to return a positive test even though he was asympomatic and showed no signs of having the virus.”