Alexander said the government would do “all we can to support the sector and take the brakes off growth”.
Gatwick wants to relocate its northern runway, which is currently used only for taxiing or in emergencies, and says it could be completed and operational by the end of the decade.
This would cost an estimated £2.2bn and would be a privately financed project.
The expansion plans are controversial and some MPs, local authorities and residents are strongly opposed.
Alexander made her comments during a speech at the annual dinner of trade body Airlines UK in London on Tuesday evening.
“I have no intention of clipping anyone’s wings. I am not some sort of flight-shaming eco warrior. I love flying – I always have,” the transport secretary said.
Alexander also raised the issue of climate change an extreme weather events.
She said she did not want a world “ravaged” by this but wanted a world where her nieces and nephews are not denied the opportunity to travel.
“This Government believes in increasing airport capacity. We’re ambitious for the sector. But these strict criteria must be met if we are to balance the needs of today with the necessities of tomorrow,” Alexander said.
The transport secretary’s comments come as Heathrow airport reports record passenger numbers for 2024 up 6%, reaching 83.9 million.
Heathrow chief executive Thomas Woldbye said the increase underlined the need for expansion.
“2024 underscores why [Heathrow] is the UK’s gateway to growth,” he said.
Plans are being drawn up after the government backed a third runway at Heathrow – the UK’s busiest airport, in January.
Mr Woldbye said he was keen for expansion to go ahead at pace and believes with private investment, planes could be taking off from a third runway within a decade.
Environmental campaigners and local communities oppose the decision, raising concerns about pollution and noise.
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