The man is a younger brother of an influential person on the island and believed to be the man seen on a security camera near the crime scene.
Pol Lt Gen Punya Mamen, chief investigator for the murders, said on Tuesday that another man suspected of being among the attackers had already fled Koh Tao and was believed to be hiding in Bangkok.
Punya refused to reveal the name of the suspect, saying that police are questioning the man and that the police expected to arrest another man in Bangkok today.
Today was the ninth day since David Miller and Hannah Witheridge, both British, were brutally killed on the island. Both suffered head wounds and police said Witheridge was sexually assaulted.