Starc, who is missing the event in Pakistan for personal reasons, joins fellow star pacemen Pat Cummins and Josh Hazlewood on the sidelines.
Allrounders Marcus Stoinis (retirement) and Mitch Marsh (back injury) have also withdrawn from Australia's original squad.
The absence of the three frontline fast bowlers is a major blow to the team's hopes of winning the one major trophy that is not already in Cricket Australia's cabinet.
Left-arm quicks Spencer Johnson and Ben Dwarshuis have a golden chance to shine in Starc's absence, while Tanveer Sangha, Sean Abbott and Jake Fraser-McGurk have also been added to the squad named in January.
Starc is also skipping Australia's one-dayers against Sri Lanka in Colombo on Wednesday and Friday.
"We understand and respect Mitch's decision," chairman of selectors George Bailey said.
"Mitch is deeply respected for his commitment to international cricket and the priority he places on performing for Australia.
"His well documented ability to play through pain and adversity, as well as forgoing opportunities in other parts of his career to put his country first should be applauded.
"His loss is of course a blow for the Champions Trophy campaign but does provide an opportunity to someone else."
Australia's Champions Trophy campaign starts with a match against England in Lahore on February 22.
Australia won the Champions Trophy in 2006 and 2009 but failed to progress past the group stage at either of the two editions since.
"I'd be lying if Champions Trophy isn't at the front of our minds. It's a big ICC tournament for us," Smith said.
Bailey acknowledged "the squad has changed significantly over the past month on the back of some untimely injuries and the retirement of Marcus Stoinis".
"We have a range of options to shape the playing XI within the tournament depending on the opposition and conditions we face," he said.
Cooper Connolly, who made his Test debut in Galle, will be a travelling reserve during the tournament.
Smith served as stand-in skipper during Australia's Test tour of Sri Lanka, earning a 2-0 series win and earning player-of-the-series honours.
The veteran batter, who was stripped of the national captaincy as part of sanctions emanating from the ball-tampering sandal in 2018, has now been entrusted to lead the ODI side in Cummins and Marsh's absence.
Smith will play through the elbow issue he first suffered in the BBL last month and aggravated on the final day of the second Sri Lanka Test.
"It feels fine. My throwing's probably going to be limited for a little bit," the 35-year-old said.
"It feels a lot better than it did when I injured it initially during that Big Bash game. It won't affect my batting."
Australia's Champions Trophy squad: Steve Smith (capt), Sean Abbott, Alex Carey, Ben Dwarshuis, Nathan Ellis, Jake Fraser-McGurk, Aaron Hardie, Travis Head, Josh Inglis, Spencer Johnson, Marnus Labuschagne, Glenn Maxwell, Tanveer Sangha, Matthew Short, Adam Zampa. Travelling reserve: Cooper Connolly.
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