Superintendent John Price said police were called to the office about 8.45am.
"The man failed to gain entry to the office and fled the scene in a vehicle," he said.
Police stopped the vehicle about 9.15am as it travelled along Ferry Road near the intersection with Ensors Rd.
After a short foot chase Moulton was arrested without incident.Nobody was injured but the Linwood WINZ was closed while police spoke with staff and early today all other WINZ offices were placed in lock-down.
The incident came a month after the first anniversary of the fatal shooting at the Ashburton Winz office.
Peggy Noble and Leigh Cleveland were killed in the September 1, 2014 shooting on Cass St.
Russell John Tully has been charged with the murder of the two women, as well as the attempted murder of Lindy Curtis and Kim Adams.