Ten moderately priced midsized cars got the institute's highest rating. They were the Honda Accord, Chrysler 200, Dodge Avenger, Ford Fusion, Kia Optima, Nissan Altima, Subaru Legacy and Outback, Suzuki Kashai and the Volkswagen Passat.
Toyota's Prius v gas-electric hybrid wagon also performed poorly on the new test, but still earned a "Top Safety Pick" designation.
"Toyota's engineers have a lot of work to do to match the performance of their competitors," IIHS President Adrian Lund said in a statement Thursday.
Toyota said in a statement that IIHS has raised the bar with the new test, exceeding U.S. government requirements. But the company said it will respond to the challenge. "We are evaluating the new test protocols and can say that there will not be one single solution to achieve greater crash performance in this area," the statement said.
Through November, Toyota has sold more than 373,000 Camrys in the U.S. It is the top-selling car in the U.S. almost every year.
Both the Prius v and Camry performed well in moderate front-end crash tests, as well as on side impact, roof strength and rear impact tests, the institute said.
Moderately priced midsized cars outperformed midsize luxury cars in the new test, the institute said. The only midsize luxury cars to earn a "Top Safety Pick-Plus" award were the Acura TL and Volvo S60.
IIHS is a nonprofit research group funded by auto insurance companies. It develops crash tests to cut deaths, injuries and property damage losses from car and truck crashes.
10 midsized cars get highest rating
Honda Accord, Chrysler 200, Dodge Avenger, Ford Fusion, Kia Optima, Nissan Altima, Subaru Legacy and Outback, Suzuki Kashai and the Volkswagen Passat.