At least three other members of the board, including Wattana Tiengkull, also quit, said Pol Lt Gen Pharnu Kerdlarpphon, adding that he was also one of them.
They did not give specific reasons for the move but Pol Lt Gen Pharnu said he personally would like to make way for change.
Pongsak Semsan, a board vice-chairman, confirmed that he had not resigned.
Since the May 22 coup, the junta has made clear its intention to revamp the boards of state enterprises as it believes many are stacked with people closely linked to politicians.
In the case of AoT, Sqn Ldr Sita was known to be close to the Shinawatra family, which controlled the Pheu Thai Party that formed the now-ousted civilian government.
AOT, 70% owned by the Finance Ministry, runs Thailand's six main airports — Suvarnabhumi, Don Mueang, Chiang Mai, Hat Yai, Mae Fah Luang Chiang Rai and Phuket International Airport. Its market capitalisation was 278.57 billion baht as of Thursday.
Shares of AOT closed at 195.50 baht on Friday, up 0.50 baht, in trade worth 482.64 million baht.