Coles had originally been expected to leave the team after Saturday's clash in La Plata and miss their final Rugby Championship test against South Africa in Johannesburg on Oct. 4.
The team, however, said on their Twitter page he had already left for New Zealand to attend the birth.
Local media reported that if his partner Sarah gave birth this week there was the possibility Coles could rejoin the team in South Africa.
Veteran Keven Mealamu is expected to step into the starting role against the Pumas with Harris, the only other specialist hooker in the squad, to come onto the bench.
It is the second time the All Blacks' preparations during the Rugby Championship have been affected by players leaving earlier than expected.
Centre Conrad Smith missed the first test against Australia in Sydney after his wife went into labour.
It is also the second disruption coach Steve Hansen has had to face this week with flyhalf Aaron Cruden dropped for their final two matches in the southern hemisphere competition after he was late for the flight to Argentina on Sunday following a night out drinking.
(Reporting by Greg Stutchbury; Editing by Justin Palmer)
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