Church of the Venerable Bede in West Road, Benwell, closed after a fire extinguisher was used to smash its windows and damage the main hall.
Food bank manager Michael Nixon said about 1,000 families missed getting food parcels due to the vandalism.
He said a glazier firm had offered to fix the damage for free.
Mr Nixon said the project had also received Â£2,500 in donations.
He said: "We are limping along and are in disarray after having to close for a few days, which meant hundreds of families missing out.
"When I saw the damage I felt like I'd been kicked in the stomach.
"But now my faith in humanity has been restored - a glazier firm has offered their services for free and they will come next week to repair our windows."
Mr Nixon said vandals carried out three separate break-ins in a week and were probably looking for cash to steal.
He said they also "mindlessly" smashed up the hall causing Â£2,000 worth of damage.
As well as food parcels, the bank also provides dozens of free, hot meals every day.
The parcels contain enough food for nine meals and are given out to between 40,000 and 50,000 families a year.
I, Daniel Blake tells the story of a man who ends up being plunged into poverty and losing his disability allowance after being diagnosed with a heart problem.
Director Ken Loach filmed scenes at the bank for the film, which went on to win the prestigious Palme d'Or at Cannes and the Bafta for Best British.

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With the score 1-1, victory on Saturday would mean Andy Murray could win the best-of-five tie for Great Britain in Sunday's first reverse singles.
Jamie Murray and Dom Inglot were originally named to face Lleyton Hewitt and Sam Groth.
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But captain Leon Smith exercised his right to change the line-up.
"Everyone in the team wants to play, everyone wants to try and help where they can," Andy Murray said on Friday.
Jamie Murray has reached the last two Grand Slam finals, at Wimbledon and the US Open, with Australian partner John Peers, while Inglot reached the semi-finals in New York with Sweden's Robert Lindstedt.
Britain captain Leon Smith had said he would not decide on his line-up until after Friday's play, saying he needed to "talk to Andy", but he has now opted for the pairing who secured a four-set victory over Nicolas Mahut and Jo-Wilfried Tsonga in the quarter-final against France.
Murray, the world number three, thrashed Thanasi Kokkinakis 6-3 6-0 6-3 in Friday's first singles match against Australia, before Bernard Tomic beat Dan Evans 6-3 7-6 (7-2) 6-7 (5-7) 6-4.
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Australia captain Wally Masur admitted his side were feeling the pressure ahead of the crucial third rubber.
"The locker room is pretty tense because I guess we thought it would be 1-1 and it's come to that situation, where there's so much focus on the doubles," he said.
"Everybody knows how pivotal that match will be but we're very happy to be in it."

The number of people claiming unemployment-related benefits now stands at 43,500.
It reverses June's increase in the number of jobless - which had been the first jump in 28 months.
However, Northern Ireland's unemployment rate of 6.5%, remains above the UK average.
The figures also show that long-term unemployment continues to be a problem in Northern Ireland.
Northern Ireland's rate of 59% is well above the UK average of 31%, while youth unemployment is also higher.
Enterprise Minister Jonathan Bell welcomed the fall in unemployment claimants, but said the levels are back to where they were a year ago.
"The latest figures reiterate the continued challenges faced by the Northern Ireland labour market and the impact of continued uncertainty in global markets," he said.
"The Northern Ireland unemployment rate [6.5%] is above that for the UK [5.6%], however, it continues to compare favourably to the April 2015 rates for the European Union [9.6%] and the Republic of Ireland [9.8%].
"In the face of these challenges it is important local businesses continue to seek new foreign investment and export opportunities."
A food bank featured in the Bafta award-winning film I, Daniel Blake, which was forced to close due to a vandal attack, has reopened.
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Andy Murray will team up with his brother Jamie for Saturday's crucial doubles match against Australia in the Davis Cup semi-final.
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Unemployment in Northern Ireland fell by 400 in July, according to the latest government figures.