Police closed the road just north of the junction with the A684 after emergency services were called to the scene of the crash at around 5.45am today.
North Yorkshire Fire Service said crews from Thirsk and Northallerton had been involved in the response.
A spokesman said the drivers of the vehicles had both been injured, with one of them suffering head, chest and leg injuries.
"Crews used hand tools to clear path up an embankment to remove casualty to a waiting ambulance before being transported to hospital via road," he said.
Also in news: This was the jacket worn by unidentified man found dead in Yorkshire reservoirSgt Paul Cording, a member of North Yorkshire Police's Road Policing Group, later shared images of the damaged vehicles on Twitter.
He said: "pologies if you were caught up in the tailback on the #A19Northbound at #Ellerbeck earlier. Drivers of the tractor and minibus both taken to hospital with serious but non life-threatening injuries.
"Huge thanks to the off duty firefighter first on scene who provided initial first aid and my #999Family colleagues who are utter professionals in situations like this. Proud to work alongside them."