Randi Zuckerberg has alleged that a man seated next to her on a flight sexually harassed her repeatedly. But when she told a flight attendant, her complaint was brushed off.

Zuckerberg, CEO of Zuckerberg Media and sister of Facebook CEO Mark Zuckerberg, tweeted a letter she sent to Alaska Airlines' CEO Brad Tilden, relating the incident.

Zuckerberg said she was seated in first class on a three-hour Alaska Airlines flight from Los Angeles to Mazatlan on Wednesday. The man seated next to her started talking "about touching himself, kept asking me if I fantasised about the female business colleague I was travelling with, rated and commented on the women's bodies boarding the aircraft."

After she complained, however, flight attendants told her the man is a frequent flier, and that she shouldn't "take it personally."

She was offered a change of seat too, but decided later she shouldn't be the one having to move.

"I'm even more furious with Alaska Airlines for knowingly and willingly providing this man with a platform to harass women...[and] being more concerned with taking his money than for the safety and security of the other passengers around him," she wrote.

About an hour and a half after she tweeted her letter, which got nearly a thousand shares in the time, Zuckerberg posted an update saying Alaska Airlines has temporarily suspended the passenger's frequent traveller status, and are conducting an investigation.

Most people reacted in disgust, with many applauding Zuckerberg for coming forward so publicly.

But some cynical commenters said it could be Zuckerberg's influential status that got Alaska Airlines to react so swiftly.