Zhang Guang Jin, 47, boarded Vietnam Airlines' flight VN595 from Hong Kong to Ho Chi Minh City on June 23.
Zhang was spotted by another passenger, Sarina Xuan Than Phan, when he was allegedly going through her luggage in the overhead bin during the flight.
When she questioned his act, Zhang pretended that it was a mistake and turned to the luggage of yet another fellow flier, Chen Chii Hwang.
After the plane landed in Tan Son Nhat, Phan informed Hwang about Zheng's suspicious act.
Hwang checked her luggage and said she had lost US$620 (VND13.8 million).
The incident was reported to the flight crew and Zheng was held by the airport authorities, who searched his property by did not find the money.
They suspected Zheng may have passed the stolen money to an accomplice who boarded the same flight.
Tan Son Nhat Airport police station is now handling the case.
According to Vietnam Airlines, theft of passengers by Chinese perpetrators on its flights is becoming more frequent.