Court, now a church pastor, complained Thursday the carrier's support of marriage equality conflicted with her views and "leaves me no option but to use other airlines where possible for my extensive travelling".
The 24-time Grand Slam champion's comments, published in a letter to The West Australian newspaper, sparked criticism on social media, including from fellow legend Navratilova.
"Maybe it's time to change the name of the Margaret Court Arena then... And I guess Margaret will be taking the boat on her next trip?:)," she tweeted.
Court has long held strong views against homosexuality, which have previously been slammed by Navratilova and Billie Jean King, who are both gay.
Her latest remarks came just weeks after Qantas chief Alan Joyce was smashed in the face with a lemon meringue pie by a devout Christian in a gay marriage protest.
Prime Minister Malcolm Turnbull brushed aside calls to rename the arena -- a key fixture of the Australian Open Grand Slam.
"Whatever people may think about Margaret Court's views about gay marriage, and she's entitled to have them ... She is one of the all-time greats and the Margaret Court Arena celebrates Margaret Court the tennis player," said Turnbull, who favours marriage equality.
Australian player Casey Dellacqua, who is gay, tweeted: "Margaret. Enough is enough," alongside an image of a letter by Court in a newspaper after the birth of her first child in 2013.
The 74-year-old had written of the "sadness that I see that this baby has seemingly been deprived of his father".
Tennis Australia and the operator of the Margaret Court Arena -- Melbourne and Olympic Parks -- distanced themselves from her anti-gay marriage stance.
The arena added that "Melbourne & Olympic Parks does not support Margaret Court's comments and we remain an organisation committed to embracing equality, diversity and inclusion".
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