The faulty shift lever has been found to occasionally slip out of the park position, which "could result in a vehicle roll-away," Toyota said.
"There were 21 minor accidents and two included minor injuries," Toyota spokeswoman Cindy Knight told AFP.
"The minor accidents involved some minor property damage. The injuries are on the order of bruises."
A lock on the shift level generally prevents the vehicle from moving out of the park position unless the brake is depressed. But Toyota found this lock could become damaged and is contacting customers to inspect and replace it.
There are also 300 affected Siennas in Germany and 100 in Guatemala, Knight said.
The recall affects model years 2004, 2005, 2007, 2008 and 2009.