The Moscow Architecture Preservation Society (MAPS) issued the warning after the future of the 1929 Constructivist gem was unexpectedly thrown into doubt following the death of architect Konstantin Melnikov's son Viktor.
The 91-year old, who lived in the house for more than three decades to protect it from redevelopment, died on Sunday, triggering a fierce legal battle to take control of the property.
It is understood Viktor's daughter Elena is claiming she owns half the house - even though she lost a court case in December over her rights to the home.
She is being supported by Viktor's nephew Alexei Ilganayev, who already owns the other half of the house.
However, according to Viktor's will, his half of the house is to be left to the state, so that it can be restored and converted into a federal museum.
Clem Cecil, the co-founder of MAPS, fears the executor of the will - Elena's older sister Ekaterina - will come under increasing pressure to bow to Elena's demands.
This could open the door to other parties becoming interested in the property.
There are concerns that, without the help of the cultural ministry, the home could be bulldozed or badly converted like many of Moscow's other 20th century architectural treasures.
Cecil said: 'The story is unfolding at the moment, but there is one rich man sniffing around already and we don't know if he is a force for the good or the bad.
'I have let him know the world is watching.'