The flight attendant accused the executive, who she did not identify, of harassing her over a six-year period, and said she had been forced to appeal to the government because "Air India refused to deal with the matter seriously".
An Air India spokesman declined to comment, saying the complaint was an "internal matter".
The incident comes at a time when women across the globe are recounting tales of sexual harassment and assault through the #MeToo global social media campaign. Several powerful men in the film industry, politics, entertainment and business have been accused of sexual misconduct and abuse of power.
In her letter, which was addressed to Civil Aviation Minister Suresh Prabhu and Prime Minister Narendra Modi and tweeted on Tuesday, the cabin crew member said she was a "proud single mother" working for Air India, but was "denied positions and privileges" after she "rejected his advances".
Mr Prabhu replied on Twitter, saying he has asked the chairman and managing director of the state-owned carrier to immediately address the issue, adding: "If necessary, will appoint another committee."
The flight attendant described the executive as a "predator" and alleged other women at Air India had suffered similar experiences.
"I used the internal processes because I did not want to attract publicity or attention, in the media or (to) the airline, but six years of torture and nine months of torturous delay and cover-ups have left me frustrated," she wrote.
A company source, who did not want to be named due to the sensitivity of the issue, said the airline had around 10 complaints of a similar nature pending.
India put in place a law five years ago that aims to ensure safety for women working in both the public and private sectors. Under the act, detailed guidelines were issued to employers to prevent or deter sexual harassment and to set up processes to resolve, settle or prosecute such cases.
Modi's government is currently trying to sell its 76 percent stake in loss-making Air India. The government said on Wednesday it received no bids so far ahead of a May 31 deadline.
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