The prime minister insists customers shouldn't bear the cost of the billion- dollar levy, saying Dr Henry was merely standing up for his own bank.
"He knows as well as I do that the banks can well afford to pay this," Mr Turnbull told ABC radio on Tuesday.
The former Treasury secretary says the tax will cost NAB more than $300 million a year.
"The government should have acted more responsibly and explained on budget night that this tax will be borne by bank customers and/or shareholders," Dr Henry told The Australian.
"There should be an open public inquiry because the tax lacks policy coherence both in respect of tax policy and in respect of financial system regulation."
Big banks hit back at government over levy
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Dr Henry, who chaired a tax review which led to the failed resources super- profits tax under Kevin Rudd, said such an impost would have helped Australia.
But the banks tax is bad for shareholders and customers, he said.
"This levy will be borne by customers right across the economy -- retail customers and business customers -- and there certainly will be an economic impact.
"No question."
Cabinet minister Steve Ciobo acknowledged Dr Henry was well-intentioned.
"However he is also not infallible," he told ABC radio from Hong Kong.
Mr Ciobo cited the design of the initial mining tax would have resulted in taxpayers refunding coal miners and iron ore miners for losses in recent years.
"So I think that there is some policy work historically that hasn't been ideal."
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Mr Turnbull insisted the levy was a fair contribution to budget repair from some of the most profitable banks in the world.
"I can see there's obviously complaints about it from the big banks - you'd expect that - but it's very similar to levies of this kind in other countries," he said.
The prime minister also rejected claims of hypocrisy by West Australian Nationals leader Mia Davies, who said Mr Turnbull was critical of her party's plan for a mining tax.
"The hypocrisy of saying no we don't think you should be asking the miners in Western Australia to pay their fair share, but then having the same rationale for slamming it onto the banks we find a little bit hard to swallow," she said.
Mr Turnbull said his levy on liabilities was different to a super-profits tax on the big miners, which pay royalties.
