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The minister has decided that the 1958 Royal National Theatre Studio - originally the Old Vic Annexe - by Lyons Israel Ellis, should be Grade II-listed.
The building, near Waterloo in south London, is considered by many to be one of the purest forms of the British branch of the Brutalist movement.
As the earliest architect-designed theatre workshop ever built in Britain, it brought together scenery workshops, wardrobe stores and offices, previously inconveniently dispersed around London, on a single site adjoining the Old Vic.
Lammy said there was an overwhelming case for listing, an argument supported by English Heritage.
'The studio is considered an important example in Britain of 'New Brutalism', an architectural development of the mid-twentieth century characterised by massive form and scant exterior decoration,' Lammy said.
The studio has historical significance too. Its association with the Old Vic, the home of the National Theatre until 1976, also adds strong group value.
'And, as the only architect-designed theatre workshop in Britain, there is a good case for giving it the extra protection that listing affords,' he added.