Clarke, who has had a five-month layoff since leading Australia to a 2-1 test series triumph in South Africa, experienced pain in his left hamstring during the team's first training session on Friday.
The 33-year-old, who has battled a chronic back problem throughout his career, suspected the lack of rest after a 15-hour flight from Sydney to Harare may have caused the injury.
"What I've learned through my career is that I probably need more time than most in regards to the gap between getting off a plane and training at full intensity," Clarke told reporters in Harare.
"If it means I have to fly a couple of days earlier than the boys on the long trips, then that's what I've got to do. It's hard because I'm a big believer in travelling with the team, I've always liked that."
Clarke will have more time to rest up before being required to play on Australia's next trip, a Pakistan series in the UAE next month which opens with a Twenty20 match, a format he has given up at international level.
"Generally when I travel to the UK, there aren't too many times that I haven't got injured at the start of the series and I'm normally at my most vulnerable at the start of a series," Clarke added.
"So I think I've got to be smarter with that, or at least try and work out how I can travel with the team but also do what's best to make sure I can play the first game."
Australia coach Darren Lehmann believed Clarke had a 50/50 chance of making the team for the opening game of a tri-series tournament that also features South Africa.
If Clarke misses out, top order batsman Phillip Hughes, a late replacement for injured all-rounder Shane Watson, could take his place while vice-captain George Bailey will lead the side.
