A vandal or vandals set light to a bin behind the Sue Ryder shop in Benefer Way, King's Lynn, on Sunday afternoon.
Flames spread to a skip where furniture donated by supporters was being stored, before firefighters put out the blaze.
Sue Ryder spokesman Paul Martin said: 'The shop has only been open two years and it's the second attack we've had.
'There's no physical damage to the shop but the fire's burned a bit of the back door. The last one cost us over £8,000 so we can safely say it's cost us thousands of pounds.
'I don't think they're targeting us, it's just mindless vandalism.'
Mr Martin said the fire had left the shop short of stock and it was now appealing for donations.
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