The temporary venue, situated in the National Theatre square, was recognised for "its daring explorations in showcasing studio theatre companies". The prize of £2000 will be matched by the National and be given to a visiting company to the venue.
The Shed, which opened in April, will be taken down next year when the refurbished Lloyd Dorfman theatre (formerly the Cottesloe) is reopened.
It was shortlisted alongside the Gate Theatre, Open Court at the Royal Court, the Union Theatre, and the Ustinov Studio at the Theatre Royal Bath.
Other Empty Space winners this year included Southwark Playhouse, which won the £1500 Mark Marvin Rent Subsidy Award, and Simple8 Theatre Company, which picked up the Peter Brook/Equity Ensemble Award of £2000.
Elsewhere, the £2000 Dan Crawford Innovation Award went to Battersea Arts Centre for its "unique use of space in converting the entire building to original development of new works from scratch to finish". And the Peter Brook/Mobius Award (£1000) was given to The Yard in Hackney for its "determined efforts to support early development of new companies and artists in an original space of a needy area of Hackney Wick".
The UK's longest-serving artistic director, the Orange Tree's Sam Walters, who steps down next year after 42 years at the helm, was honoured with a Special Achievement Award.
"[Walters] originated the revival of undiscovered plays, which are staged and produced with top-drawer actors in the round," said a press statement. "Such high standards of professional work has brought to the local audiences of Richmond enormous gratification as well as to varied London audiences."
A Special Achievement Award was also given posthumously to Robert Robson, the Lowry's artistic director who died earlier this year at the age of 58.
The selection panel for the awards included critics Lyn Gardner, Dominic Cavendish, Mark Shenton, Fiona Mountford, Andrzej Lukowski and awards founder Blanche Marvin.
Winners were announced during a lunchtime ceremony held at the National Theatre Studio.
The Empty Space Awards, now in their 24th year, are presented in recognition of the pioneering work that, in the spirit of the legendary director Peter Brook, is achieved by smaller venues that receive "comparatively little or no public funding".