Starc was replaced in the Melbourne Test by Jackson Bird, who failed to take a wicket in a pace combination with Josh Hazlewood and Pat Cummins.
The opening day of the Boxing Day Test drew more than 88,000 spectators last week, despite Australia having already clinched the five-match series with victories in Brisbane, Adelaide and Perth.
Agar is most likely to join forces with Nathan Lyon in a two-man spin attack at the SCG.
Smith started out his career as a leg-spinner but decided to concentrate on his batting and has quickly established himself as the world's leading batsmen.
The Australian captain delivered another masterclass in concentration and discipline by occupying the crease for more than seven hours.
It became an issue at the MCG on Friday after the umpires, Sundaram Ravi and Kumar Dharmasena, spoke to England captain Joe Root and Jimmy Anderson, and Australian television repeatedly showed footage of Anderson cleaning the seam on the ball.
Trailing by 164 runs after England's first innings ended on 491 on the first ball of the day, Australia had crawled to 103 for two in their second innings when play was suspended before tea because of the storm.
This was Alastair Cook's fifth double ton of his career and his highest score against Australia.
Alastair Cook became the first Englishman since Wally Hammond to score a double hundred at the MCG (in 1928) and his 244 not out is now the highest score made by any player against Australia in Melbourne.
Alastair Cook, who had struggled badly in the first three tests, prompting speculation about his future in the team, was at his imperious best.
With the left-arm Starc ruled unfit for Melbourne, Jackson Bird was recalled to play his first test in a year.
Take a look at some of the highlights that went down in the 4th Test between Australia and England at Melbourne.
When play ended on day one, Australia was sailing along at 244 for three in its first innings with Smith not out 65 and Shaun Marsh with him on 31.
Handscomb was dropped from the Australia squad for the third Test at WACA in Perth.
Australia will be without pace spearhead Mitchell Starc, who is out with a bruised heel.
The right-handed batsman, who has scored 5,499 runs for England in Test cricket at an average of 52.37, also said the "little boy" tag does not go with him and he knows what he can do on the field.
Curran, an uncapped right-arm bowler, was only added to England's Ashes squad when Steve Finn was ruled out at the start of the tour due to injury.
The 29-year-old was hit by a stray ball from a Cameron Bancroft shot that ricocheted off the net structure and struck him on the right hand.
Tom Curran, Mark Wood and Mason Crane are the bowlers who are likely to replace Overton.
The left-arm bowler had performed his menacing best in the recent times, having grabbed 19 wickets in three matches to become the top wicket-taker in the series.
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