The Australian No.10 failed a head injury assessment against Argentina in Townsville on Saturday, in what was Lynagh's return from a concussion suffered against the British and Irish Lions.
The 22-year-old will miss next Saturday's rematch in Sydney while Schmidt said there would naturally be doubts around his availability to face the All Blacks later this month.
"We gave him an extended rest after the third Test against the Lions and he felt good after that game and feels good now," Schmidt said.
"That's a good first sign, but we know he can't play next week and puts him in a bit of doubt for the Bledisloe.
"We won't be risking him in any way, shape or form and getting him the best medical advice."
James O'Connor was impressive in his final-quarter cameo on Saturday as Australia won 28-24 thanks to a try six minutes into injury time.
The veteran started in both Tests in South Africa, with Tane Edmed called in as cover with Noah Lolesio (neck) a long-term absentee and Ben Donaldson battling an adductor injury.
O'Connor will remain with the squad for next week's Test but could then be forced to depart for club duties after signing with Leicester in England.
"That'll be, can I call it, 'by negotiation'," Schmidt grinned after the Townsville win.
Schmidt's wry smile came because the new Leicester coach is his recently departed Wallabies assistant, Geoff Parling.
"He's massively supportive, but has a responsibility to Leicester," Schmidt said.
"So I know he's available next week and beyond that it'll be conversations with Geoff."
Lynagh has struggled for consistency in his short career due to repeated niggles and head knocks.
He's suffered at least two additional concussions in the previous two Super Rugby Pacific seasons.
But Schmidt said the brave playmaker was doing what he could to protect himself and revealed he had only left the field on Saturday because of a tight hamstring.
"His tackle technique is usually pretty sound," Schmidt said.
"We brought him off for a tight hamstring and it was after that they decided to do a HIA.
"Tom didn't flag it. I'm guessing it's from a mouthguard alert."
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