In the new shootout session, the American driver did enough with the 11th fastest time in SQ1 to make it through to the second qualifying segment, but struck the wall at Turn 15 late on.
The impact with the barriers on the downhill exit damaged his car and included his right rear corner being ripped off, but Sargeant suffered no injuries.
Despite there being several hours between the end of qualifying and the start of the sprint to try to make repairs, Williams has run out of time to get it fixed.
The FIA announced just two hours before the start of the sprint that Williams had requested Sargeant’s car be withdrawn from the sprint – which the governing body accepted.
Sargeant’s absence means that the grid will be closed up, so all drivers qualified from 16th to 20th will move up one position.
Williams said that it tried all it could to get Sargeant’s car fixed before for the sprint but unfortunately there was not enough time to complete the work.
The team posted on social media: “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 Subsequently we have withdrawn Logan from the Sprint.
“Gutted for Logan who has shown great pace with two Q2 appearances this weekend.”
The disappointment of missing the sprint comes on a weekend when Sargeant appeared to have made some progress with his qualifying form as he made it through to Q2 for the first time this season.
He is due to start 15th for the Grand Prix on Sunday, just two places behind his team-mate Alexander Albon. Williams should be able to complete the repairs by then.