DETROIT - According to the National Highway Traffic Safety Administration, the investigation started last week and includes cars from 2001 to 2006 model years.
The agency says a faulty cruise control cable may be the cause, as it can detach and hold the throttle open.
NHTSA reported at least two drivers said their cars took off and ran red lights and they were only able to stop them by shifting into neutral or putting the vehicle into park.
Ford is looking into how many complaints dealers have received.
The NHTSA will use the data to determine how may cars had the same parts and whether the problem is widespread enough to demand a recall.
There have been no recalls so far.
If you own a Ford Taurus you can call Ford at 1-866-436-7332 with questions about the vehicle.