The West Midlands officer and two other men are being questioned on suspicion of conspiracy to pervert the course of justice.
Police said they were given "false and malicious information" suggesting an officer was to "be kidnapped as part of a terrorist plot".
West Midlands police were put on high alert because of the hoax.
The three Birmingham men are questioned by anti-terrorism and anti-corruption teams.
The 28-year-old officer at Birmingham West & Central Local Policing Unit has also been arrested on suspicion of misconduct in a public office and misuse of police systems.
The other men, aged 25 and 31, are also being questioned on suspicion of conspiracy to commit misconduct in a public office.
The force issued an alert to officers and staff after receiving the anonymous tip-off on 8 December last year.
It urged them to take extra precautions, including not wearing uniform during journeys to and from work.
"At a time when the national threat level was severe, the threat was considered credible and police acted swiftly to protect officers and police staff," a police spokesman said.
The three men are being questioned by detectives from West Midland Police's Anti-Corruption Unit, with support from the Counter Terrorism Unit.
A 31-year-old man, who was arrested on the day of the offence, was eliminated from inquiries and has been deported.

The Grade II-listed Drummond Mill on Lumb Lane in Manningham was ravaged by a fire which started in the basement on Thursday.
The building has now been partially demolished to prevent further collapse.
Historic England said West Yorkshire's mills are "important landmarks which need to be cherished".
The organisation, which preserves and lists historic buildings, is currently part-way through a review into West Yorkshire's mills to establish best practice for future redevelopments.
Spokesperson Deborah Wall said: "The community is deeply affected and emotional about the loss of this historic building.
"It just shows how important these landmarks are to people and why the work to find ways to capture the stories of these places and to cherish them is so important."
Last month, property consultants Cushman and Wakefield began work with architects and Historic England to examine ways in which West Yorkshire's vacant textile mills could be brought back into use.
Trevor Mitchell, Historic England's planning director for Yorkshire, said: "West Yorkshire's textile mills are iconic buildings that people care deeply about.
"Some have been brilliantly and creatively converted into places to work, live or socialise.
"We are working to understand how these successful conversions have been achieved and try to find solutions for those mills that need a new purpose to become great landmarks in our region again."
Successful redevelopments include Tower Works and Marshalls in Leeds, Sunny Bank Mills in Pudsey, Lister Mills in Bradford, Salts Mill in Saltaire, Red Brick Mill in Batley, and Dean Clough in Halifax.
Yorkshire has 172 listed textile mills.
Ms Wall said the future of Drummond Mill was "totally uncertain" until Bradford Council and the fire service had determined the full extent of the damage.
Three men, including a police officer, have been arrested following a hoax terror plot to kidnap an officer.
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A fire which destroyed a Bradford mill has "underlined the urgency" of working to preserve West Yorkshire's mills, Historic England has said.