Williams down to one car for Australian GP after Alex Albon crash
Albon hit a wall then bounced onto another one via the kerbs towards the end of the first session at Melbourne's Albert Park.
He was not hurt but was unable to compete in second practice, with the team confirming late Friday the chassis was badly damaged and that they did not have a spare.
Team principal James Vowles said Albon had a better chance to score their first points of the season during Sunday's race, meaning Sargeant was sidelined.
"While Logan should not have to suffer from a mistake that he did not make, every race counts when the midfield is tighter than ever," he said.
"So we have made the call based on our best potential to score points this weekend."
Sargeant said missing out was "the hardest moment I can remember in my career".
"I am however completely here for the team and will continue to contribute in any way that I can this weekend to maximise what we can do," added the US driver.
Anglo-Thai driver Albon, who scored 27 of the team's 28 points last season, said he was gutted about the situation.
"Logan has always been a consummate professional and a team player from day one, and this won't be an easy one for him to take," he said.
"At this point though, I cannot dwell on the situation and my only job now is to maximise our potential this weekend."