The pilot in question, who has not been named, took a photo of former prime minister Yingluck Shinawatra together with her son and entourage while they were walking to board the aircraft.
He then posted it in a group chat with around 30 pilots and wrote: "Here come our victims."
Another pilot -- believed to be from another airline -- responded: "Perhaps CFIT should be arranged."
CFIT stands for "controlled flight into terrain" and is used to describe a scenario when a pilot in control of an aircraft crashes it.
The news broke Sunday after a screen grab of the pilot chat group was leaked.
A controversial figure in Thai politics, Yingluck was on her way back from a visit in the northern province of Phrae where she met with supporters.
When she was inaugurated in 2011, she became Thailand's first female prime minister and its youngest in over 60 years. She was ousted in 2014
by a coup.
The person who wrote the message is being investigated, Nok Air told CNN.
"Nok Air would like to apologize to Ms. Yingluck Shinawatra and we feel deeply sorry for the inappropriate action of our pilot," Nok Air CEO Patee Sarasin said in a letter addressed to Yingluck.
"We hope this letter can show our sincere determination to explain and to show our strong disagreement with any negative attitude of our airline staffs toward customers," he added.
On Monday, Yingluck responded on Facebook.
She thanked them for the statement but said, "Hopefully, this kind of incident will not happen again not only with me but with other passengers as well in the future in order to maintain a professionalism, confidence, and the standards of the organization."