The doors, floor and the roof of the wooden car are in a state of decay but the Occupation Museum doesn't have enough money to refurbish it, say representatives.
The car is a replica built after photographs of the cattle wagons in which people were deported from Latvia to Siberia on June 14, 1941.
More than 40 people were loaded onto each of cars and were taken thousands of kilometers away from Latvia after the 1940 Soviet Union's occupation of independent Latvia.
"At the moment we cannot even open the door as they're in a state when you shouldn't touch them at all," said Ziedonis Grigorjevs of the museum.
The commemorative car was set up in 1996 and after 20 years of exposure to the elements it is time to refurbish it. It would cost around 20 to 30 thousand euros according to estimates by the museum.
The museum has sent a letter to the Riga City Council and Latvian Railways asking for help in restoring the important monument.
There were two main waves of deportations, one in the wake of the Soviet Union's 1940 occupation of independent Latvia, which saw more than 15,000 people (including 2,400 children under the age of ten) loaded into cattle trucks on June 14, 1941.
Families were separated. Some children never saw their fathers again. There were numerous deaths during the journey of thousands of kilometers in cramped, unsanitary conditions.