The company said it would monitor the situation in Ohio and said its assembly plant in Illinois would be closed for the second shift.
General Motors Corp idled plants at six locations in four states, while Ford Motor Co temporarily shut plants in five locations.
Among the Ford closures was the Chicago assembly plant that makes the all-new Ford Explorer SUV and the Ford Taurus and Lincoln MKS sedans.
A Subaru plant in Indiana that builds the Camry sedan for Toyota Motor Corp was also shut because of the storm and Toyota canceled the first shift at a plant in Princeton, Indiana, which builds the Sienna minivan, spokesman Mike Goss said.
Everything else is running right now, but it is a very fluid situation, Goss said in an e-mail. We are monitoring suppliers.
Four Honda Motor Co Ltd plants in Ohio are also closed, as well as a plant in Indiana, which builds the Honda Civic sedan.
All plants made it through Tuesday OK, but today is another matter, Honda spokesman Ed Miller said.
Automakers keep few parts on hand in their assembly plants to contain inventory costs.
But the same just-in-time system for managing inventory means they are sometimes forced to idle entire plants and thousands of workers when a single part runs short because of a supplier or shipping problem.
Now, as automakers seek to ramp up production to meet burgeoning demand, some auto suppliers are coming up short, having cut capacity during the downturn.
Ford and Chrysler both idled plants last week due to parts shortages.
In Canada, Chrysler's minivan plant in Windsor, Ontario, was already closed this week because of a parts shortage. Last week, Ford idled the plant where it makes its best-selling F-150 pickup trucks due to a shortage of engines that are made at a Ford plant in Cleveland.
(Reporting by Deepa Seetharaman and Bernie Woodall; editing by Gerald E. McCormick, Maureen Bavdek, Gunna Dickson and Andre Grenon)