The auto giant says the brackets could corrode and break off from the frame.
California is not included in the recall, but if you own a Passport, you may want to check with your dealer.
Honda says it has received more than 30 complaints from owners, but no injuries have been reported.
The recall covers SUVs in Connecticut, Delaware, Illinois, Indiana, Iowa, Kentucky, Maine, Maryland, Massachusetts, Michigan, Minnesota, Missouri, New Hampshire, New Jersey, New York, Ohio, Pennsylvania, Rhode Island, Vermont, West Virginia and Wisconsin.
Owners can determine if their vehicle needs inspection by going to www.recalls.honda.com or calling 800-999-1009 and selecting option 4.
The Associated Press contributed to this report.
