The unnamed suspects were detained just before 7am at their homes by officers investigating alleged newspaper breaches of privacy, reports BBC News.
The male journalist was arrested in Kent and is to be interviewed at a police station in the county.
The 58-year-old man, who is not said to be a reporter, was arrested in Surrey and taken to a police station in south London.
They were both arrested under Section 3 of the Computer Misuse Act 1990 and Sections 1 and 2 of the Regulation of Investigatory Powers Act 2000.
It is said to be part of Operation Kalmyk, a sub-operation of the Operation Tuleta probe into alleged computer hacking by journalists.
Sixteen arrests have been made so far under Tuleta, and the initiative runs alongside the Operation Weeting and Operation Elvedon probes into phone hacking and illegal bribes respectively.
> Ex-'NOTW' legal adviser Tom Crone arrested in hacking probe
The overall police investigation into journalism-related crimes was set up in the wake of the phone hacking scandal at the now defunct News of the World tabloid paper.
Last month, a trial date in September 2013 was set for various former News of the World employees who stand accused of hacking-related offences, including ex-editors Rebekah Brooks and Andy Coulson.
They face various charges related to the alleged interception of voicemails belonging to up to 600 high profile individuals, including politicians, celebrities and murder victims.