The company said no major layoffs would occur among the plant's 1,000 employees, though it was unclear whether that might signal smaller-scale cutbacks or unpaid temporary leaves of absence.
Dmitry Medvedev, Russia's president, visit the assembly plant in Shushary near St Petersburg in November.
The $300m venture was initially set to produce 60,000 cars a year.
Yekaterina Kulinenko, a spokeswoman for Ford, said it would also be shutting down its St Petersburg area factory until July 13.
Foreign car makers had rushed to tap the country's rapidly expanding middle class after years of prosperity fuelled by oil revenues.
Russia was on the way to become Europe's largest car market, with sales rising some 25 per cent annually, but the downturn in the economy has caused car loans and other credit to all but dry up.
Rising unemployment has also helped curtail the market's rapid growth.
New car sales in Russia dropped 47 per cent in the first five months of 2009, compared to a year ago, the Association of European Businesses said.