The first national strike in the health service for 18 years is to go ahead next Thursday.
NHS Logistics supplies medical equipment and food to the NHS
The health service union Unison announced hundreds of workers in the agency NHS Logistics will walk out for 24 hours.
The protest, over the sell-off of the network to German firm DHL, could lead to English hospitals running short of vital equipment.
But the government said it believed any impact would be limited.
A second 24-hour strike is also planned, the date of which will be announced early next week.
Further industrial action will follow.
Around 900 staff were balloted by Unison and of the 66% who voted, 74% backed a strike.
Hospitals have to order equipment three days ahead and have limited space to store stockpiles.
NHS Logistics supplies around 50,000 lines of products, including bedpans, latex gloves, syringes, bandages, medical equipment and food.
The strike decision was taken at a meeting held on Friday afternoon in Alfreton, Derbyshire - the site of one of the agency's five depots.
Sense of loyalty
Karen Jennings, Unison's Head of Health, said: "Our members have a very strong sense of loyalty to the NHS and have worked hard to make NHS Logistics a highly-competitive, innovative service.
"Last year it delivered savings to NHS trusts of £2.8 million that can be ploughed back into front-line services.
"NHS Logistics has a fantastic track record on innovation and awards for efficiency. There can be absolutely no justification for privatising this service."
She said Unison also had proceedings issued for a judicial review this month.
"We're taking every avenue, every process possible to try and stop what we think is a very destructive move by this government."
The government believes the DHL deal, which comes into force at the start of October, will help save £1bn over 10 years.
But Unison views it as a sign of "creeping NHS privatisation".
The union said it expected any action to hit the supply of goods to hospitals, but added it had agreed emergency plans to cover life-saving equipment.
The Department of Health said most hospitals also had their own supply and delivery arrangements and would be able to "cope with demand".
A spokesman said: "The NHS used around 500,000 different products such as catering supplies, office equipment and medical supplies but only around 51,000 of these products are provided by NHS Logistics.
"The majority of hospitals have their own local supply and delivery arrangements.
"The impact of a one-day strike is not expected to cause significant disruption to NHS operations.
"The impact will be similar to coping with a bank holiday.
"However, we have put detailed contingency plans in place to ensure minimum disruption to NHS services in the event of industrial action."