"This is a disaster. About 30% of the theater roof has been destroyed. The stage is covered with water from the melting snow as well as the underground deposits where we keep the sets," the director of the theater, actress Maia Morgenstern told AFP.
"I am very worried because this theater is a historical monument but also a very important element to preserve the Yiddish culture in Europe", added the actress, known for her role as the Virgin Mary in Mel Gibson's "The Passion of the Christ."
The State Jewish Theater is one of the few living remains of the once vibrant Yiddish culture in Eastern Europe.
Located in the centre of Bucharest, in a district that was home to more than 300,000 Jews before the Holocaust and the Communist dictatorship, it features plays in the Yiddish language.
The theater opened in 1940 and was allowed to continue its activities during the Second World War, sheltering Jewish actors and playwrights banned from other cultural institutions.
Romanian authorities said they would provide assistance in getting the building repaired.
"An expert will tell us as soon as possible how to secure the roof", the municipality of Bucharest told AFP by email.
A full restoration plan has been approved and will last 18 months. In the meanwhile, the troupe will be offered the chance to relocate in another theater.
Between 280,000 and 380,000 Romanian and Ukrainian Jews died in Romania and the territories under its control during pro-Nazi marshal Ion Antonescu's regime, according to an international historians' commission headed by Nobel Peace laureate Elie Wiesel.
Romania's Jewish community today counts just over 3,300 people, according to the official census.
The first professional Yiddish theater troupe in the world was founded in Romania in 1876 by Abraham Goldfaden.
Romania has been hit with heavy snowfall in recent days, forcing the closure of schools and highways in the southeast of the country and disrupting train services on Wednesday.