The money will bolster the £16m already pledged by Arts Council England towards the £25m cost of repairing and maintaining the arts venue.
The announcement has come ahead of a public consultation on the proposed alterations to the site.
Earlier this month, the Southbank Centre failed to close a skatepark beneath its Queen Elizabeth Hall.
The closure was due to form part of a planned £120m redevelopment of the entire site, which comprises the Royal Festival Hall, Queen Elizabeth Hall, Purcell Room and Hayward Gallery."
