The shock move comes less than a month after Ms Hrdlicka moved from chief executive of Jetstar to heading up Qantas' booming loyalty business.

The dual Australian and New Zealand-listed a2 Milk announced the appointment to both stock exchanges on Thursday morning.

She will replace a2's current CEO, Geoffrey Babidge, and is expected to start at the beginning of the 2019 financial year.

"I am delighted to be joining the very talented and accomplished team at The a2 Milk Company as their new CEO," Ms Hrdlicka said in a statement.

"This is a strong, principled company with significant opportunity ahead and impressive momentum in each of its core markets."

Ms Hrdlicka joined Qantas in 2010 as head of strategy and technology and became CEO of the Jetstar Group in 2012.

She spent five years leading the budget airline during a period of rapid expansion into Asia, particularly Japan.

Qantas in August announced an executive reshuffle in which Ms Hrdlicka was moved to lead the airline's lucrative loyalty business, with Qantas International boss Gareth Evans taking the reins at Jetstar.

The pair only started their new roles last month and it is understood Ms Hrdlicka told chief executive Alan Joyce she was resigning late on Tuesday. She will leave Qantas in March.

The former Bain & Company partner was previously a non-executive director of Woolworths and had reportedly put up her hand for the CEO position there - a role Brad Banducci eventually claimed.

She was also widely speculated to be a front-runner with Mr Evans to take over as Qantas CEO if and when Mr Joyce resigns.

Her departure firms up Mr Evans as the heir apparent at the national carrier, but also gives credence to comments from chairman Leigh Clifford that Mr Joyce is not going anywhere soon.

Mr Joyce said Ms Hrdlicka had made a "tremendous contribution to the Qantas Group, and particularly to Jetstar".

"She leaves with our best wishes for her next challenge," he said.

Qantas said a replacement to lead its loyalty business would be made next year.

A2 praised Mr Babidge for his "outstanding contribution'' to the business, adding that he was instrumental in establishing and leading a2 in Australia a decade ago, and had been in his present role since 2010.

"The Company has achieved unprecedented growth during this time due primarily to his leadership in developing and executing a bold strategic vision and in skilfully managing the phases of growth achieved to date,'' a2 said in a statement.

Mr Babidge said Ms Hrdlicka had the key attributes that a2 was seeking in a CEO ''in spades'', a very good track record in business and ''highly relevant'' experience with Woolworths.

''She was seen, obviously by us, to be the ideal candidate,'' he said.

''We're actually quite a different company, we're not a traditional dairy, agri or quite frankly FMCG (fast-moving consumer goods) company. We operate outside the square, we need to, we're somewhat a disruptor and we've got very good people who can run the business operationally day to day.

''So because of those factors, we did not necessarily see a depth of past experience in dairy, or agri for example, being particularly necessary,'' he said.

Mr Babidge, 64, said he had ''no plans at this stage'' on what he would do next after his departure from a2. But he also said it would be ''unlikely that I would take on another full-time CEO role''.

The announcement about Mr Babidge's departure comes at a time with a2 a $5.3 billion company by market capitalisation, with growing sales and profits, and with strong backing from investors.

This year alone, the company's stock price has more than tripled. Shares in a2 rose 24 cents on Thursday, to close at $7.31. Last month a2 reported a 138 per cent jump in net profit to $NZ52.3 million ($47.4 million) for the first four months of fiscal 2018.

''The company's in great shape, I've effectively had 10 years in my current role and building the company, and I believe for both the company and myself it's an opportune time to consider transition,'' Mr Babidge said.