The former Lions coach, 70, was taken by ambulance to Wellington Hospital.
McGeechan, a former pupil of Leeds Beckett University who played for Headingley and is currently Executive President at Yorkshire Carnegie, has been working as part of Sky Sports' team covering the Lions tour in New Zealand.
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, offered an update to her father's condition on Twitter.
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 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."