UPDATE: The woman has now been successfully talked down from the bridge and the road has re-opened. Delays are expected.
The closure affects both carriageways between junction 22 for Denshaw and junction 24 for Ainley Top.
The woman is believed to be on the 120ft-high Scammonden Bridge.
Police negotiators are currently in dialogue with her.
The incident comes just days after a man died after falling from a nearby bridge at Rishworth. He passed away on Thursday.