The burglary happened between Thursday evening and Friday morning, and a back door window was smashed to gain entry.
Pictures show items strewn across the floor and a broken electrics box, while shelves for toiletries and food left bare.
Claire Matthews, who runs the Hope For Food bank in the West Howe Industrial Estate, told Sky News: “We think one month’s worth of food is gone, but also toiletries – and we’re talking about 100 families who have missed out.
“They have take all the toiletries for the guys living on the streets too, like wet wipes.
“We have had clothes donated, they are all gone.
“Nappies, which we have been saving for certain families coming out of bed and breakfasts, the supplies for a disabled man leaving hospital, all gone.”
Ms Matthews said the response from the community had been amazing, but warned it could take two to three weeks to restock the food bank to its previous level.
She added: “We have even had one chap from France hear about it and promise to help.
“We have plenty of beans and soups but it’s other things we need.
“Even a joint of meat, worth about £60, that was donated for meals for the homeless was taken.”
The volunteers discovered a camouflage baseball cap with an NY logo on the front following the burglary, which they believe may have been left behind by a perpetrator.
Posting on Facebook, the team wrote: “We are all heartbroken and reduced to tears to turn up at our unit today to find it broken into and vandalised.
“Most of our stores of vital clothing, shoes, food, toiletries and other household items have been taken. We just can’t believe people would do such a cruel thing.
“We need coffee, biscuits, long life milk, long life juice, squash, tinned fruit, tinned meat, hot dogs, spaghetti, dried and microwave rice, tinned veg, jam, pasta sauce, ketchup, mayo, cereal, rice pudding, custard, deodorant, shower gel, toothpaste, toothbrushes, hand wash, wet wipes, shampoo, moisturiser, sun cream.”
They also need men’s boxers, jeans and hoodies.
Hope For Food has five drop off points around the city for donations.
Police are investigating. Anyone with information should contact Dorset Police with reference 22-143.