Tauranga police Senior Sergeant Shannon Clifford said the threat was made to the IRD call centre.
''Something was said in the head of the moment with reference in what happaned in Ashburton,'' Mr Clifford said.
''Winz and IRD took it upon themselves to close their doors. That's something they decided to do for their safety and protection.''
Yesterday, several police units converged on Courtney Rd after a man was reported to be carrying a gun in the vicinity of the Greerton Winz office. The slug gun was recovered by police, who said the incident was the result of ''heightened awareness'' following Ashburton.
''Any threats to government agencies or in reference to Ashburton are going to be treated seriously and prosecution is likely.''
The arrested man is expected to appear in Tauranga District Court on Thursday.
Peg Noble and Leigh Cleveland were killed and colleague Lindy Curtis was injured when a gunman opened fire at their Ashburton Winz office on Monday last week
Russell John Tully, 48, has been charged with two counts of murder and one of attempted murder and has been remanded in custody to appear in the High Court at Christchurch on September 23.