Starc will miss the game following the passing of his father Paul on Tuesday after a battle with cancer. Starc's wife Alyssa Healy also withdrew from New South Wales' next two WNCL fixtures.
Earlier in the season Starc left Australia's hub during the limited-overs matches against India to spend time with his family but returned to feature in all four Tests.
"All our thoughts and prayers are going out to Mitch and his family," said team-mate Nathn Lyon said. "It's a tough time for Mitch but he knows he has all our love and support from, just not me, but from everyone here at New South Wales Cricket and the cricket community as well."
Smith will miss the clash, which was relocated from Melbourne to Sydney, due to an elbow issue that has flared up.
"I have had some pain in my elbow that's gradually worsened since the Test against India at the SCG and it requires some rest and rehab," Smith said. "I am hoping I will be right to travel with the Blues to Adelaide for our games down there next week but we will have to see how it responds to treatment."
Lyon said Smith had been struggling to hold the bat at training. "He tried to have a hit yesterday. He was just in discomfort, pain. All I know is it mustn't be great if he's missing a game of cricket, especially for New South Wales."
Pat Cummins will make his first Shield appearance of the season after missing the game against Victoria last week. Josh Hazlewood is being rested. Liam Hatcher and Jason Sangha have been included in the 13-man squad as replacements for Smith and Starc.
New South Wales Shield squad: Peter Nevill (capt), Sean Abbott, Harry Conway, Trent Copeland, Pat Cummins, Moises Henriques, Daniel Hughes, Nick Larkin, Nathan Lyon, Kurtis Patterson, Jason Sangha, Daniel Solway, Liam Hatcher
Alex Malcolm is a freelance writer based in Melbourne