"The exception to the disappointing pattern is the 2015 Toyota Sienna, which earned an acceptable rating," the IIHS said. "It joins the Honda Odyssey, which last year earned a good rating."
The Sienna and Odyssey, which was tested earlier, earned the IIHS "Top Safety Pick+" award.
The Institute did not rate the Kia Sedona minivan.
"The manufacturer has told the IIHS it plans to make a change to the vehicle in the coming weeks to improve small overlap protection, so it will be tested shortly," the Institute said on Thursday.
IIHS' small overlap test replicates what happens when the front corner of a vehicle collides with another vehicle or an object such as a tree or a utility pole.
"Minivans are popular among parents, a group that tends to be safety-conscious, but we've only seen two so far that offer decent protection in small-overlap crashes," said David Zuby, the Institute's executive vice president and chief research officer.
The National Highway Traffic Safety Administration has not rated the 2015 Sienna, Quest or Sedona. The 2015 Honda Odyssey earned the top five-star overall safety rating from NHTSA. The 2015 Chrysler Town & Country and its sibling, the 2015 Dodge Grand Caravan earned four-star overall safety ratings from NHTSA.
Edmunds says: Some critical safety information for any family considering some of the most popular minivans in America.