The animals - all under two months old - had been drugged and put into cages in the man's suitcases, police said.
The suspect, a 36-year-old man from the United Arab Emirates, was trying to board a flight from Bangkok to Dubai.
Several people are thought to be involved and an investigation into a trafficking network is under way.
The man was seized by undercover police at Bangkok's Suvarnabhumi International Airport while he was waiting to check-in as a first-class passenger.
Officers had been monitoring him since his black market purchase of the rare animals, said the Freeland Foundation, an anti-trafficking group based in Thailand.
There were two leopards, two panthers, an Asiatic black bear and two macaque monkeys in the man's luggage.
"It looked like they had sedated the animals and had them in flat cages so they couldn't move around much," said Steven Galster, director of Freeland, who was present at the arrest.
Some of the animals were placed inside canisters with air holes.
"It was a very sophisticated smuggling operation. We've never seen one like this before," Mr Galster said. "The guy had a virtual zoo in his suitcases."
Last month, Thai customs officials seized 1,800 protected lizards said to be destined to be sold as food.
The Bengal monitor lizards, stuffed into blue mesh bags and hidden behind fruit, were found in southern Thailand near the Malaysian border.
Lizard meat is valuable and seen as a delicacy in parts of Asia.