The stretch between the A57 at Mottram and A616 at Langsett is affected.
M62 is closed both direction to high sided and vulnerable vehicles between Junction 22 at Saddleworth and Junction 24 at Huddersfield, along with the A66 in Cumbria and Durham, between between the A685 at Brough and A67 at Bowes.
A Highways England spokesman issued a warning to all motorists with gusts of 70mph forecast across the north.
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He said: "Road users are advised to take extra care when driving today as strong winds are currently being experienced in the North of England."
The Met Office has issued a weather warning for South Yorkshire today, with strong winds expected between 1am and 11am.
A Met Office spokesman said: "A spell of very windy weather is expected during Wednesday, with the west to northwesterly wind likely to gust 60mph in places, locally 75mph over high ground.
"Some disruption to road travel is likely, including restrictions on bridges.
"The strongest winds will affect some of the higher level roads, for instance those over the Pennines and the Southern Uplands.
"However, the northwesterly winds will also be very strong and gusty at lower levels too, including in areas to the east of high ground."
Church Street in Sheffield city centre is partially blocked near to Leopold Street because of a fallen tree.
Trees in Sheffield blew over on Bents Green Road, Bents Green; Mickley Lane, Totley; Dore Road, Dore; Rochester Road, Lodge Moor; Shirecliffe Road, Shirecliffe and Roscoe Bank, Stannington.
Earlier today there was traffic chaos on Penistone Road, Owlerton - one of the busiest roads during rush hour - because of a fallen tree near the Hillfoot Road junction.
Council workers have also been called to fallen trees on Moss Way, Waterthorpe, Ringinglow Road, Bents Green; Cart Road, Chapeltown; Clay Wheels Lane, Wadsley Bridge; More Hall Lane, Bolsterstone and Fulwood Road, Fulwood.
In Sheffield city centre, police have cordoned off part of Armadillo Storage at West Bar, because of cladding coming off in the wind this morning.
Paradise Street, next to the storage centre, has been closed because of objects falling from buildings.