The 74-year-old team chief has been a tetraplegic and confined to a wheelchair since a car crash 30 years ago
The 74-year-old team chief has been a tetraplegic and confined to a wheelchair since a car crash in France 30 years ago, but amazed and inspired his family, team, friends and paddock colleagues, not to mention fans and a wider public, with his energy and determination.
Word of his illness came during a news conference at the Autodromo Hermanos Rodriguez ahead of this weekend's Mexican Grand Prix where one of his team's former drivers, German Nico Rosberg has a chance to win his maiden drivers' title.
The Williams team's chief executive Mike O'Driscoll said: "Frank was taken ill at Monza (in September). He's had a tough time in hospital. He's contracted pneumonia. He is making a slow and steady recovery."
O'Driscoll was deputising for Williams's daughter Claire Williams, the deputy team principal, at the event because she had decided to remain at her father's side.
"We hope to see him back at Grove (Williams' base) very soon. We all know how determined he is," added O'Driscoll of one of the most popular figures in the sport.
"We expect Claire to be back at a race. She has wanted to stay close to home, close to Frank, but in this modern world, you're never more than a phone call away.
"So we stay connected. She is part of everything that happens on a minute-by-minute, day-by-day basis. We hope to see her by the end of the year. Hopefully, that will be in Abu Dhabi (the final race on November 27)."
Under Williams's guidance with fellow-founder technical director Patrick Head, the team has won nine constructors' championships and seven drivers' titles, the last claimed by Canadian Jacques Villeneuve in 1997.
Briton Damon Hill won the title with Williams in 1996.
Williams was taken to hospital two years ago because of a pressure sore and made a full recovery.
The team are scheduled to announce their 2017 driver line-up on Thursday having re-signed Finn Valtteri Bottas. He is expected to be partnered by Canadian rookie Lance Strol.
This season the team are in a battle for fourth place in the championship with Silverstone-based Force India after finishing third for the last two years.
"I'd like to give a lot of credit to Force India as they have done a superb job bringing the fight to us and making the battle more interesting than we would have liked," said O'Driscoll, echoing the dry wit of Williams, who was honoured with a knighthood in 1999 and has also been made a Chevalier of France's Legion d'honneur.
"We haven't given up the fight for fourth place and we intend to get it back in the remaining three races."