McDonald was unable to fly out as scheduled and will isolate for seven days before joining up with the squad. He is expected to be with the side before the second T20I on June 8.
This will be McDonald's first tour since being appointed full-time into the head coach role after he took over from Justin Langer in an interim capacity earlier in the year which included the tour of Pakistan.
Ben Sawyer, the assistant coach with the Australia women's team, had been due to be part of the A-team coaching staff but he is expected to be confirmed as the new head coach of the New Zealand women's set-up in the coming days.
The latter stages of Australia's tour of Pakistan were hit by Covid-19 when Ashton Agar, Josh Inglis and physio Brendan Wilson tested positive during the white-ball leg.
The first T20I against Sri Lanka takes place on June 7 with the opening two games back-to-back in Colombo before the tour moves to Pallekele.
The Australia T20I squad, which is missing Pat Cummins (rested) and Adam Zampa (paternity leave) from its first-choice players, will gather in Colombo on Thursday.