More than 4000 Inland Revenue Department and Ministry of Business, Innovation and Employment staff will go on strike next month.
Staff at both agencies will strike for two hours on July 9 and July 23.
"Our members are very reluctant to take this step, but they feel they have no choice - and the level of support in the vote shows the level of frustration," Public Service Association (PSA) national secretary Glenn Barclay said.
The PSA claimed Inland Revenue's IT system cannot process the new Best Start tax credit which kicks in next week as part of the Government's Families Package and it would have to be done manually.
"Our members take their jobs very seriously and they're trying desperately to keep the system on track while IR presses ahead with its Business Transformation project which will see 1 in 3 staff let go by 2021.
"It starts on 1 July, and members are told they will have to process this manually, drastically increasing their workload," PSA national secretary Erin Polaczuk said.
"To have all this happening while the employer refuses to consider a modest across-the-board pay increase is deeply upsetting to our members."
The notice of strike action comes as nurses prepare to strike next month.Nurses around the country will strike for 24 hours on July 5 and again on July 12.
The country's primary school principals and teachers are also voting on whether to take industrial action, in August. Those results are not yet known