The motorway is closed westbound between junctions 24 at Ainley Top and 21 at Milnrow and eastbound it is closed between junctions 20 at Rochdale and 22 at Saddleworth.
Highways England said the closure is in place for safety after gusts of wind were expected to reach 90mph and will re-open when wind speeds drop.
A number of other roads are also closed including the A635 Holmfirth Road, A6024 at Holme Moss and the A58 at Ripponden. The B6114 at Saddleworth and the A640 New Hey Road.
The A62 Huddersfield to Oldham is open and passable with care but not recommended for high sided vehicles.
Police say a diversion is in place from junction 24, following the black circle route, which will take you along the A629, A646 to Todmorden, A6033 to Littleborough and join the A58 to the A664 following signs for the motorway to Junction 21
Chief Insp Michael Brown, of West Yorkshire Police, said: “We are working hard with our colleagues from Greater Manchester Police, Highways England and other emergency services and organisations to get things moving.
“We would like to thank members of the public for their patience during the disruption and remind them that the closures are in place for their safety. If anyone is in urgent need of assistance they are asked to phone 101."