China Eastern Airlines said passengers affected by the cancellations include businesspersons, tourists and students.
"At this time, they said themselves they don't want to apply".
In its statement, China Eastern expressed disapproval of the Taiwan government's decision to withhold approval, and said many experts had been consulted and found no existing safety issues with the new routes.
Mainland Affairs Council Minister Chang Hsiao-yueh said China's decision to put the four routes - M503, W121, W122, W123 - into effect hurt Taiwan's aviation safety and national security and added to challenges between the two countries.
The CAA's move was made in response to China's unilateral decision to launch four new commercial air routes in the Taiwan Strait, including a northbound M503 route, on January 4, and the two Chinese airlines' use of those new routes in the following weeks.
Amid all these rows, China Eastern and Xiamen Airlines had planned 176 round trips extra over the Lunar New Year holiday which now stand canceled leaving thousandsof passengers stuck.More news: Syria opposition missing from Russia's Sochi talks
The new passenger routes come close to airspace used by Taiwanese airliners and military planes, at a time when Chinese military drills encroaching on Taiwan's airspace have become increasingly common. Then direct flights were permitted, and they continue across the Taiwan Straits today.
Taiwan's Ministry of Transportation and Communications (MOTC) said it could arrange military aircraft in Kinmen for Taiwanese people who wished to return to Taiwan from China during the Lunar New Year after the mass cancellation of cross-strait flights.
China and Taiwan divided amid civil war in 1949 and Beijing threatens to use force to take control of the self-governing island republic.
The refusal to agree to the extra flights is being seen as retaliation from Taipei, after China opened up several new air routes - which both China Eastern and Xiamen Airlines have been using.
"Yesterday I met a relevant official from the International Civil Aviation Organization, and he said the M503 route has been assessed and approved of by them, it's safe and reliable", Wang said, referring to the main disputed route.