The left shoe, made for Fox in his role as Marty McFly, is part of the film's pair of self-lacing Nike Air Mags.
The 1989 sequel sees McFly and Dr Emmett "Doc" Brown travel to a futuristic 2015, where shoes have 'power laces'.
The money raised will go to Fox's foundation for Parkinson's research.
Fox launched his Michael J Fox Foundation after being diagnosed with Parkinson's disease in 1991.
