Alvarez Isnaji said he had negotiated the group's release, along with that of a second cameraman who was freed last week, after making "token payments" to the alleged abductors.
Statements from the freed captives "unravelled the fact that Mayor Alvarez Isnaji is involved in the kidnapping," Razon said.
Razon said police have also arrested Mameng Bitaw, a man who allegedly agreed to guide the journalists to an interview with a senior Islamic militant leader in Jolo.
Bitaw went missing while on the way to the rendezvous and the journalists were subsequently captured, Razon said.
National government officials said no ransom was paid to the hostage takers but sources close to the negotiations said more than $400,000 was paid to secure the captives' release.
Isnaji said he paid $4,500 to the abductors for the victims' "board and lodging" - a euphemism for ransom.
He did not say who provided the money.