Starc, who is Australia's leading wicket-taker in the series with 19, bruised his heel bowling in Australia's series-clinching third Test win in Perth last week.
There wasn't enough time for him to recover from the injury to his landing foot, with team management officially ruling him out two days before Tuesday's Melbourne Test.
While Starc had been optimistic about his chances of playing, Australia's selectors took a cautious approach with their star paceman ahead of a key series against South Africa early in the new year.
Starc said he hoped to return for the series-ending Sydney Test on January 4.
"It's never nice to miss but it would be pretty selfish of me to go in to a game not at 100 percent," he told reporters.
"It's nice that we have won the series and we can play it a little bit safer now.
"I think the discussions (with selectors) lasted about 30 seconds... and it gives me a good chance now to have a bit of time off it over the next few days and give me a really good chance for Sydney."
Starc's withdrawal continues his run of bad luck in the Melbourne Cricket Ground showpiece. He has played in just one Boxing Day Test since making his debut in 2011.
Last year Starc scored 84 with the bat and took a match-sealing four-wicket haul in a final-day win against Pakistan there.
Bird said he was ready for his first Test in a year.
"I've been ready to go for 12 months basically," he told reporters.
"I had a week in the Perth nets working on a few different things with bowling coach David Saker.
"It'd be unbelievable to play an Ashes Test on Boxing Day."
Meanwhile, wicketkeeper Tim Paine is expected to play after joining his teammates at training on Sunday after initially remaining at home in Hobart after his father-in-law suffered a stroke.
First Published: December 24, 2017, 9:36 AM IST