The coronavirus, which was first detected in the central Chinese city of Wuhan late last year, spread over the Lunar New Year holiday, which would normally be one of the busiest times for regional airlines.
Instead dozens of international carriers have reduced or suspended flights to China in a bid to halt the pathogen's spread and as passenger numbers fall off a cliff.
In his video message to employees, Tang warned Cathay was experiencing "one of the most difficult Chinese New Year holidays we have ever had" because of the virus.
"And we don't know how long it will last," he added. "With such an uncertain outlook, preserving our cash is now the key to protecting our business." He announced a series of measures to tackle the crisis, including asking staff to voluntarily take unpaid leave.
"I realise this is difficult to hear. And we may need to take further steps ahead. But by supporting the special leave scheme, you will be helping at our time of need," he told staff.
He also asked suppliers to reduce their prices and said the airline would make short-term adjustments to its capacity, including an already announced move to reduce flights to the Chinese mainland by 90 per cent.