Sargeant was one of several drivers suffering from severe dehydration and heatstroke during what has been described as the most physically demanding race in recent times.
The American rookie was initially keen to push through, but after consulting with his team he opted to retire on lap 42.
Among others, Sargeant was checked and released by F1's medical staff, with his condition compounded by illness in the build-up to the Losail race.
"Following Logan's retirement from the Grand Prix, he has been assessed and cleared by the medical team on-site after suffering from intense dehydration during the race weakened by having flu-like symptoms earlier in the week," Williams said in a statement.
The Grove team said Alex Albon was also checked in the medical centre after struggling to get out of the car in parc ferme and having to be supported by his mechanics.
"Alex was taken to the medical centre to be treated for acute heat exposure. He has now been assessed and cleared by the medical team."
The race on the hot and demanding high downforce circuit was made even harder by the mandated three tyre stops, which forced drivers to push flat out from the first lap until the last.
Aston Martin's Lance Stroll nearly fainted while getting out of his car and stumbled to a nearby ambulance for help, while Alpine driver Esteban Ocon admitted to being sick behind the wheel.
"We’re pleased to report that everyone is okay after today’s Qatar GP," said Aston Martin.
"It was absolutely brutal, by far the most physical race I've ever experienced," said Mercedes man and GPDA director George Russell.
"I felt close to sort of fainting in that race, I've never experienced anything like it before.
"I asked my engineer to give me encouragement just to try and take my mind away from it.
"I do a lot of heat training in the sauna, so you push your body to the limit, and sometimes you just need to get out of that sauna. That's sort of how I felt from about lap 20.
"I opened my visor for the whole race, and it was hot air, but it was better than no air."
Additional reporting by Matt Kew
