Sargeant clouted the barrier at Turn 15 late in the opening phase of the three-part qualifying session.
The American never made the apex of the 90-degree left-hander towards the end of the lap and found the wall on the corner's exit.
It left him with hefty damage to the FW45, specifically the right-rear wheel.
“Logan's car will not run in the F1 Sprint this afternoon despite the best efforts of the team,” Williams confirmed on Twitter.
“After receiving the FW45 back following the shootout, we worked flat-out on the car but there is not enough time to complete the repair.
“Subsequently we have withdrawn Logan from the Sprint.”
With Sargeant absent from the Sprint, the grid behind where the 22-year-old would have started will be closed up.
While Sargeant's withdrawal leaves 19 cars set to participate in the Sprint, only 18 will do so from the grid.
Alpine elected to remove Esteban Ocon's car from parc ferme conditions after he suffered an exhaust leak during the Sprint Shootout.
As a result, the Frenchman will start the F1 Sprint and tomorrow's grand prix from the pit lane.
Similarly, his empty grid box will also be filled.
Logan's car will not run in the #F1Sprint this afternoon despite the best efforts of the team. 😔
After receiving the FW45 back following the shootout, we worked flat-out on the car but there is not enough time to complete the repair. Subsequently we have withdrawn Logan from… pic.twitter.com/cy8Q1nerww
— Williams Racing (@WilliamsRacing) April 29, 2023