The GMB union said over 100 members will strike from Friday February 9 at 00.01am until Saturday February 10 at 11.59pm.
However, Asda has said that just 46 of the store’s 225 colleagues voted for industrial action and the grocer believes there will be minimal disruption to operations.
The company also said it has been actively trying to resolve the dispute with offers that have been “continually rejected” by the GMB.
Workers have been in dispute with Asda bosses over a “toxic” working environment but have previously held off from striking to allow time for talks.
Members of the GMB then balloted again this month and voted for strike action after rejecting Asda’s latest offer.
It is not yet known what proposals Asda put forward during the crunch talks.
GMB regional organiser Nicola Nixon said: “GMB members voted to stand up to their employer in December and they’ve done it again in January and February.
“Counter proposals have been made to the company to settle the dispute but Asda has failed to come back with any improvements.
“We originally gave Asda until Tuesday [February 6] as a show of goodwill but no improved offer materialised and so our strike will now go ahead.
“Our members are determined to stand up to Asda and their management and say enough is enough.
“They should be able to come to work without threat of bullying or putting their health, safety and wellbeing at risk.”
An Asda spokesperson said: “We have met the GMB on several occasions recently, including mediation at Acas, to try and agree a fair solution for all colleagues in Gosport.
“The proposals we put forward include the appointment of an independent third-party organisation to establish the facts regarding GMB’s complaints and report back jointly to both parties.
“Unfortunately, this proposal was rejected by the GMB membership. As most Gosport colleagues are not members of the GMB and will continue to work as normal during this period, we are confident there will be minimal disruption to our operations.”