PCS claims that Fujitsu is refusing to increase a below-inflation pay offer - of between 1.5 percent and 2.5 percent - to its workers, while senior management have received large bonuses as a result of performance targets being met.
Industrial action would affect work on contracts across the UK, including those at the Home Office, Ministry of Defence (MoD), and the Office of National Statistics.
The balloted IT workers are members of the Public and Commercial Services (PCS) union, which said that HM Revenue and Customs (HMRC) and the Driver and Vehicle Licensing Agency (DVLA) would be particularly affected by strike activity.
Fujitsu provides IT support to HMRC's systems, and maintains the IT systems that produce driving licenses. PCS said that the company could face financial penalties for not meeting service level agreements.
In addition to the low pay offer, the union said that Fujitsu had reneged on a commitment provided during talks last year, to introduce a structured pay progression system.
"While senior managers are pocketing bonuses in excess of what some of our members earn in a year, it's not only wrong, it's offensive for Fujitsu to claim it can't afford to increase pay.
"Just because these staff are off the government's books, ministers are ultimately responsible for what happens in their department's name and cannot simply wash their hands of issues like low pay among their contractors," said Mark Serwotka, PCS general secretary.
A spokesperson for Fujitsu said: "Fujitsu is disappointed PCS has decided not to ask its members to vote on our pay offer, which we believe is a fair one, but has decided instead to ask them to vote on whether to take industrial action.
"Fujitsu is committed to working with PCS to resolve these issues and to implement a pay review for members and indeed we are meeting with them and ACAS for further talks next week."
Fujitsu has also recently , who were protesting against the sacking of union activist Alan Jenney. This was also intended to have an impact on a number of Fujitsu's government contracts, including with the Home Office and HMRC.
Meanwhile, PCS members working in IT support at the Department for Work and Pensions are currently working to rule in response to .