A 15-year-old girl has been arrested and bailed on suspicion of arson after the attack on Wilko's Nuneaton store on Tuesday, July 8.
It is believed the fire started in the 'goods inward loading bay' and caused extensive damage to the building and stock.
A spokesman for the value retailer told the Nuneaton News that it was assisting the local authorities with their investigation into the cause of the fire.
"Our latest estimate is that it may be four to six weeks before we are able to reopen this store and we apologise to our many loyal customers for the inconvenience this may cause."
While the repair work is taking place staff at the store have been relocated to other branches.
The spokesman added: "Once the store was handed back to us by the fire service it was clear that the store would have to be closed for some time.
"The site is now safe and secure and we are sorting power and lighting requirements.
"But we need to replace or repair damaged goods lifts and we need to clean, remove or replace stock, professional contractors are lined up for such tasks."
Shoppers have been advised that their nearest Wilko store is at Hinckley, which is four miles away.
Firefighters took around four hours to extinguish the flames which started just after 12pm.