The agency will carry out an international media relations campaign and provide digital strategy for the museum.
It will also provide event management for the UK launch of the Friends of the museum, to be held in Parliament next month.
It is not clear whether Curzon was competing with other agencies to win the account but there was no incumbent.
The museum opens its doors on 9 May next year, 70 years after the end of the war.
It is intended to become an international research and education hub and will teach visitors about the contribution of Jewish soldiers in the Second World War.
It has the backing of the Israeli government and will comprise several wings that educate visitors about the armies and fighting organisations that took part in the war from 1939 to 1945, as well as the ensuing war of independence from 1945 to 1949.
Farzana Baduel, managing director of Curzon PR, said: "The Museum of the Jewish Soldier in World War II is an inspirational project that we at Curzon PR are proud and honoured to work with."