Traffic Wales said two lanes westbound between junction 30 Cardiff Gate and junction 32 Coryton were likely to remain closed for a number of hours.
Earlier 10 mile tailbacks have reduced to five miles following the crash at 06:51 GMT.
One casualty was taken to the University Hospital of Wales in Cardiff but no further details have been given.
Traffic Wales said at 11:15 GMT that lanes one and two were likely to remain closed for a number of hours, although the lengthy queue is improving.
Police have appealed for witnesses to the crash.
The crane was on the back of another lorry, emergency services said.
One motorist told BBC Wales it looked like a lorry had clipped a mobile crane and gone into the central reservation.
"The cab of the lorry has come off and is upside down on the road with a blue cover over it," he said.
"One lorry is buried in the central reservation and another two have pulled up. Looks like lorry was driving down road, has gone into the central reservation."
There are also delays reported eastbound, with drivers slowing down near the crash scene.
"South Wales Police are at scene continuing to investigate the collision," said a force spokesperson.
"At present, lanes one and two are closed. Lane three is open, however drivers are asked to avoid the area if at all possible."
South Wales Police have asked any witnesses to call 101.