Mr Jones, who is Regional Development Minister, took aim at the airline's board and chief executive after it pulled out of flights to the Kapiti Coast.
He was quickly shot down by Prime Minister Jacinda Ardern and Finance Minister Grant Robertson, who has backed up the board's need for independence.
Air New Zealand's share price, up more than 46% on a year ago, was trading up slightly at $3.38 yesterday.
But the situation raises concerns about whether companies, and in particular those with the Government as a major shareholder, are at greater risk of political interference under the Labour-led Government.
As well as the airline, the Government has a stake in the listed power companies - Mercury, Genesis and Meridian Energy.
Michael Midgley, chief executive of the New Zealand Shareholders Association, said even when it had not been the responsible minister commenting, the share prices of companies had been affected in the past.
He pointed to the listing of the power companies when the Government had been forced to change the structure of the Meridian listing after politicians talked up changes to the sector.
Mr Midgley said there were risks in politicians getting involved in appointing people to boards.
"When they are appointed for other reasons, particularly political ones, then history is not good."
But Grant Swanepoel, head of research at Craigs Investment Partners, said anyone that owned 51% of a company had influence over it and shareholders knew that.
He said the Government's 51% ownership of the energy companies was no different from Infratil being the majority shareholder in Trustpower.
"I am more concerned about political interference in the whole industry," he said.
Mr Swanepoel said Mr Robertson's views did not change his assessment of the valuation of the energy stocks, and the Air New Zealand stoush was just some of the "noise" that came out all the time.
