A major blaze broke out on the south London building where contractor Gilbert Ash is currently working on a £6m refurbishment programme.
Gilbert Ash started on the site in September with work due to be completed by January 2016 on the 15-month contract.
Culture Secretary Sajid Javid, said: “I was terribly sad to hear about the fire at the Arts Centre but was deeply relieved that no one was hurt.
“I have visited the centre to see the damage and met the very dedicated team of staff who have launched an impressive fundraising campaign and are doing everything to carry on as far as possible.
“The Arts Centre are having to divert all their available resources into dealing with the aftermath and so I am pleased to be able to confirm that Government will provide £1 million towards the ongoing redevelopment work to help get this important south London venue back on track.”
The cash comes on top of the original Arts Council England grant of £4.69m towards the redevelopment project.