The airline moved fast to comply with the demand from the Civil Aviation Administration of China (CAAC), suspending a pilot arrested during anti-government protests in Hong Kong and firing two airport employees citing misconduct on Saturday.
It also said it would bar "overly radical" staff from crewing flights to the mainland, and analysts said the tighter oversight, along with the impact the protests could have on traffic, could affect the airline's bottom line.
"Not only is this likely to affect direct China flights, but also flights to Europe and, to a lesser extent, to the U.S., given that they fly over China airspace," Jefferies analyst Andrew Lee said.
Passenger traffic in mainland China, Europe and North America accounted for over 50% of all Cathay's traffic in the first half of this year, according to Jefferies data.
Cathay's shares tumbled to HK$9.82 on Monday morning, their lowest since October 2018 and near levels not seen since the 2009 financial crisis.
Cathay's largest shareholder is Swire Pacific Ltd, with a 45% stake, followed by China's flagship carrier, Air China Ltd which owns 30%, according to the airline's latest annual report.
The company, which in March reported its first profit in three years, has seen a decline in forward bookings for travel to Hong Kong due to the Hong Kong protests.
It was not immediately clear how the regulator's directive would affect flight staffing. Cathay CEO Rupert Hogg told staff the company would report to the CAAC by Thursday on how it would improve flight safety, according to a copy of a letter seen by Reuters.
Cathay did not immediately respond to a Reuters request for comment.
The Hong Kong Cabin Crew Federation, a union representing airline employees, has criticised the regulator.
In a statement on Saturday, it said the CAAC should have "respected Hong Kong people's rights and freedoms" on the basis of the "one country, two systems" principle, which guarantees the former British colony a high degree of autonomy from Beijing.
(Reporting by Donny Kwok, Brenda Goh in Hong Kong and Stella Qiu in Beijing; Editing by Stephen Coates) ((email@example.com; +86 (0) 21 6104 1763; Reuters Messaging: firstname.lastname@example.org))