Maxwell's omission marked the first time he was left out of an Australian squad for a home series since his debut in 2012-13.
It came after a prolific start to the Sheffield Shield season, leading the competition with 590 runs at an average of 73.75 after missing selection for Australia's Ashes squad.
However, Australian captain Steve Smith told the Victorian to focus on the basics and train smarter when quizzed last week about his non-selection.
"He could train a little bit smarter," Smith said at the time.
"We've all seen the way he can come out and play and do all his funky stuff and be pretty cool with that.
"But when he puts his head down, he's actually a really good batsman, as we've seen in Shield cricket.
"If he keeps his head switched on and trains really well and focuses on basic things, probably more than the expansive things, then I think that will help him have his consistency."
Lynn's strain is the latest setback for the excitement machine, who had suffered a shoulder injury while on national duty last summer before missing the start of this year's BBL with a minor hamstring problem.
"It is annoying and I'm very disappointed to miss an opportunity with the ODI side, but I know it is minor in the scheme of things," Lynn said.
"I have been working very hard to get myself right, and the positive thing is that my shoulder is feeling very good.
"I'll do the work again and I am confident I will give myself a shot at playing some good cricket again soon."
Australia's physio Alex Kountouris said Lynn would need to prove his fitness for the Heat before he was reconsidered for selection.
Lynn is due back for the Heat around their January 27 clash with Melbourne Renegades, four days before the Australian T20 squad is scheduled to assemble for the tri-series with England and New Zealand.