The motorway has been closed in both directions between junctions 35a and 36 since the early hours of this morning.
Police initially said it was likely to remain closed until at least 3pm but that has since been pushed back to 5pm.
Highways England tweeted at around midday: “We are experiencing heavy traffic on the diversion routes for this closure, traffic on the #A61 and #A616.
“To any @EFL fans travelling in #Yorkshire please try alternate routes. @LUFC @BarnsleyFC @BCFC @SwansOfficial.”South Yorkshire Police have advised motorists where possible to use the M18 or A1(M).
Bus passengers in the area have also been warned of lengthy delays.
Stagecoach Yorkshire tweeted: “#SHEFFBUS #BARNSBUS service X2 suffering delays of up to 20 mins due to extra traffic around the Birdwell area following the closure of the M1. Sorry for any inconvenience.”