Rupert Hogg said he was taking responsibility as these had been "challenging weeks" for the airline.
Paul Loo, the Chief Customer and Commercial Officer of Cathay who was one of 57-year-old Hogg's deputies, also stepped down, the South China Morning Post reported.
In the past week, Cathay Pacific fired four members of staff - two pilots and two airport employees - for their involvement in protest-related actions or incidents.
Hong Kong has been rattled by protests since June 9, sparked by the controversy over the now-shelved extradition bill, which would have allowed criminal suspects to be sent back to mainland China.
"These have been challenging weeks for the airline and it is right that Paul and I take responsibility as leaders of the company," said Hogg.
The airline was targeted by Beijing for what was seen as its failure to rein in staff taking part in protests gripping the city over the last 10 weeks.
The carrier's Chairman John Slosar said new management was needed to "reset confidence".
"The board of directors believes that it is the right time for new leadership to take Cathay Pacific forward," the airline said in a statement.
Hogg said it was an "honour" to have led the airline group, which he did for just over two years.
Cathay Pacific said Augustus Tang - the CEO of the aircraft engineering HAECO Group - has been appointed to replace Hogg as Chief Executive, while Ronald Lam - the CEO of low-cost airline Hong Kong Express - will be its new Chief Customer and Commercial Officer.
Both have been seconded to the company by the Swire Group, which owns Cathay Pacific, HAECO and Hong Kong Express.
"Augustus Tang and Ronald Lam have the experience and depth of knowledge of aviation and our people to be strong and effective leaders of Cathay Pacific at this sensitive time," Cathay Chairman Slosar said about the newly-appointed officers.
In a note to employees, Hogg said the protests and the subsequent attention on the airline had put great stress on the company and staff.
"This is a grave and critical time for our airlines," Hogg said, acknowledging the crisis that had engulfed the company in the "all-important" mainland China market.
Last week, Cathay Pacific had told its staff it would not stop them joining the pro-democracy demonstrations currently sweeping Hong Kong.
But on Monday, Hogg warned staff they could be fired if they "support or participate in illegal protests".
Cathay faced pressure online after China's state-run press fuelled a #BoycottCathayPacific hashtag, which trended on Chinese social media.
Hong Kong International Airport, one of the world's busiest, has been closed at times this week in the wake of the massive anti-government protests that have paralyzed one of Asia's key transport hubs.
( With inputs from IANS )