The 70-year-old, who has been working as part of Sky Sports’ team in New Zealand, was taken by ambulance to hospital before Saturday’s game.
The four-time Lions head coach, who also played eight Tests for the tourists as a centre, walked himself to the ambulance before being transferred to hospital.
McGeechan’s daughter, Heather, allayed fears of any serious issues via her Twitter account.
Responding to a number of journalists, pundits and former players, Heather McGeechan (@heathermcgeech1) tweeted: “@PaulMorganrugby @robvickerman @BenKay5 spoken to my dad, Geech and he is fine, just a bug. Thank you everyone for all your best wishes x.”
Sky Sports presenter Alex Payne, speaking at half-time in the second Test, said: “He is on the mend. We’re delighted to say he’s making slow and steady progress. We hope to have him with us next week.”