The man was detained at his home in Cardiff at 7am and was being questioned at a police station in the area, police said.
At the same time it was announced that two other men had been arrested as part of the same inquiry, Operation Tuleta, last month.
On June 26 officers arrested a 53-year-old man at his home in West Sussex. He was taken to a central London police station and bailed to return in September pending further inquiries.
Two days later, a 65-year-old man was arrested when he attended a south London police station. He was bailed to return in October.
It brings to six the number of people arrested under the computer hacking probe Operation Tuleta, which is linked to the Met's investigation into phone hacking, Operation Weeting.
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Police said that none of the three were linked to any news organisation or the activities of journalists. Neither were they police officers or public officials.
The three men were each held on suspicion of suspected offences under the Computer Misuse Act 1990 and Regulation of Investigatory Powers Act.
So far, 24 people have been arrested as part of the phone- hacking inquiry, and 41 as part of an investigation into alleged corrupt payments to officials, Operation Elveden.