According to Asiana, the plane was moving on the taxi way at Istanbul's Ataturk Airport at around 5:30 p.m. local time.
No injuries were reported, but the cancellation of the Asiana flight caused inconveniences for passengers.
Nobody was hurt in the incident, it said, adding that Korean officials plan to send staff to Istanbul to investigate the incident.
There were no passengers on the Turkish plane, and none of the 238 passengers on board the Asiana flight bound for South Korea's Incheon Airport were injured.
With its customary Turkish hospitality, Turkish Airlines takes pride in curating a delightfully different experience for its passengers and going beyond expectations with its array of unique products and services.
Fire crews rushed to the scene and started a cooling process in case of an eruption of fire.
Video footage posted to social media shows the Asiana A330's right wing severing the Turkish A321's vertical stabilizer, which is left hanging off the aircraft.
Almost 100 passengers arrived in Incheon through flights offered by other carriers like Korean Air and Turkish Airlines later on Sunday.