"I'm okay," the driver reported over the radio after dipping a wheel on to the wet grass, losing control at turn three and spinning into the barriers, with the mangled car ending up in the middle of the track at the seaside Zandvoort circuit.
Sargeant, who has yet to score a point this year and has already lost his seat for 2025, was taken to the medical centre for precautionary checks.
Marshals put out the flames but the damage looked significant, with qualifying scheduled for 1500 local and the Williams mechanics likely to struggle to get it rebuilt in time.
The red flags came out after 14 minutes, with the irrepressible but soggy Orange Army of Dutch fans in the grandstands still waiting for Red Bull's home hero and championship leader Max Verstappen to do a lap.
The damp session eventually restarted with a minute remaining of the hour scheduled and drivers leaving the pits in a queue for the chance of a timed lap through the spray on intermediate tyres.
Verstappen overtook a McLaren and a Mercedes in the pitlane, crossing the white line in his hurry to exit, and was shown a black-and-white warning flag for failing to follow the race director's instructions.
Alpine's Pierre Gasly claimed the fastest lap in the meaningless session, ahead of Haas's Kevin Magnussen and Sauber's Valtteri Bottas.
Williams said Sargeant's car, which was returned to the garage while repairs were made to the barriers, had the same upgrade package as teammate Alex Albon.
"Hundreds of hours are spent on making things. The worst time is when you have just introduced some bits and you put it into the wall," Williams principal James Vowles told Sky television.
"Qualifying will be upon us pretty quickly but the car is in a pretty bad state.
"The first step of it is we will go through in detail what's been damaged. It looks pretty serious and that could result in a chassis change."
