The incident happened just before 6.30pm yesterday (Thursday, November 1) on the southbound carriageway near junction 42, which the motorist was travelling on in the wrong direction.
First reports suggested there were five vehicles involved, although there is now only thought to be two.
The driver of the second car involved received minor injuries and road was closed in both directions for several hours.
It has now fully re-opened.
West Yorkshire Police are urging anyone who witnessed the accident to call 101, quoting reference number 1697 of yesterday's date.