Sky Sports commentator Brundle – a major figure on the F1 circuit – usually does the grid walks before the race.
But Sky informed viewers on their show that he felt unwell and was taken to the medical centre at the circuit.
The broadcaster tweeted: “Unfortunately Martin Brundle has taken unwell & is in the medical centre.
"Ross Brawn did have a trophy to mark 20 years of #MartinsGridWalk."
Martin Brundle (second left) has been taken ill at Silverstone
— Sky Sports F1 ������ (@SkySportsF1) July 16, 2017
Sky host Simon Lazenby said: "We can assure you he is in good hands and we wish him well.
"I hope you're in good hands mate and you get well soon, Martin.
"In his place at short notice, Paul Di Resta is with David Croft."
Di Resta took over duties for the veteran broadcaster, who has done the grid walk since 1997.
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