The 24-hour strike will begin at 01:00 on Monday, 13 June.
Union Unite said the dispute is about the disparity in overtime payments for drivers that deliver to customers from 14 of Marshall's manufacturing sites in the UK.
While manufacturing employees receive time and half pay for overtime work, drivers only receive time and a third.
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Unite added the situation has been escalated by the fact chief executive Martin Coffey received an 87% increase in his remuneration package last year to just over £2 million a year, in addition to company profits and shareholders dividends increasing.
National officer for construction and allied trades, John Allott, said: "This vote for industrial action demonstrates a sense of anger among drivers at Marshalls over pay and the increasingly belligerent attitude of management.
"The last thing our members want to do is to take industrial action and cause disruption for the two biggest customers of Marshalls - Travis Perkins and Jewson.
"But faced with an increasingly hostile management, our members have clearly signalled they are prepared to take industrial action to achieve pay justice.
"We would urge the company to engage meaningfully with Unite to resolve the dispute and improve industrial relations for the long-term."
(LM/MH)
