It happened at about 1.45pm on the northbound carriageway between Junction 40 at Ossett and Junction 41 at Carr Gate, Wakefield.
The crash, involving a horse box containing two horses, has closed three lanes of the northbound carriageway.
Police will close both northbound and southbound carriageways soon to allow the two horses to be safely transferred.
Traffic officers and West Yorkshire Police are at the scene and queues are building on the approach to the crash.
The Roads Policing Unit tweeted: "M1 north after jct 40, RTC involving a horse box.
"We will have to temporarily close the motorway shortly to transfer the two horses. Please be patient."