The drill comes after Tsai warned last month about what she called Beijing's "military expansion" - the increase of mainland air and naval drills around the island since she came to power in May 2016 - and amid a new row over flight routes in the strait.
Tensions have been growing this month since Beijing started new flight routes in the strait without consulting Taiwan.
The airlines said Taiwan's refusal to approve the new routes leaves them no choice but to cancel all 176 flights, a claim contested by Taiwanese officials.
Taiwan, though, has objected to a new route known as M503, which it says passes dangerously close to existing airports on the Tiaoyutai Islands. Taiwan said it was done without its agreement, contravening what Taipei had said was a 2015 deal to first discuss such flight paths.
On Tuesday, the Chinese carriers China Eastern Airlines and Xiamen Air announced that they had cancelled 176 flights meant to meet added demand during the holiday since they had yet to receive approval from Taiwan's Civil Aeronautics Administration.
The airline association said Taiwan is using the M503 route "as an excuse".
The four routes were specifically designated for the strait of Taiwan which separates mainland China from the island.
The airline apologized to customers and said it was providing free refunds and rebooking for anyone booked on the now-cancelled flights. In the statement, the airline said that common interests of their consumers and their company, in general, had been severely infringed upon by the unreasonable obstruction caused by the government of Taiwan. As a result, the Taiwanese government withheld approval of route applications from the Chinese airlines.
Reports suggest about 50,000 passengers will be affected by the flight cancellations. "It's not at all that we said we didn't agree for them to apply", Ho added.
Kinmen and Matsu have both been under Taiwan's control since defeated Nationalist forces fled to Taiwan at the end of the Chinese civil war in 1949.