The coach had come to a halt in a ditch, but it was still upright and had not overturned.
Around 30 people were on board and 10 of them were treated for minor injuries while four were taken to hospital.
The driver, a 48-year-old man from Bournemouth, has been arrested on suspicion of dangerous driving and is helping police with their enquiries.
A spokesperson for South East Coast Ambulance Service, said: “Shortly after just half-past-eight we had a call from police to attend an incident where a coach had left the M3.
"We sent a total of three ambulance paramedic cars, as well as two ambulances with two paramedic crews, there was also an air road vehicle with a doctor and paramedic which stayed at the scene for 10 minutes.”
"All the injuries were minor ones like back pain, cuts and bruises. We have taken four patients in two vehicles to Frimley Park Hospital.
"Two were suffering from neck pain, one from shoulder pain and one patient had arm and shoulder pain.”
No other vehicles involved
National Express confirmed the coach was travelling from Bournemouth to London and had stopped at both Southampton and Winchester.
In a statement, a spokesman, said: “We can confirm that one of our vehicles has been involved in an incident on the M3 near Fleet and we are currently in the process of making onward travel arrangements for the customers involved.
"Emergency services attended the scene and we will help them in any investigation into this incident.”
No other vehicles were believed to have been involved. The J4A exit slip road was closed to allow for debris to be cleared and an investigation to take place, causing major delays on the M3 heading into Surrey as diversions were put in place.
Two engines from Rushmoor fire station were sent to the scene as well as crews from Yateley and Basingstoke.
A spokesman for Highways England said: “The incident happened at around 8.29am.
“The carriageway was initially blocked but... the coach has come to rest in a ditch adjacent to the carriageway. A replacement coach has been provided."
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DVSA give the punctuality requirements of local bus services in England and Wales as:
If you operate local services, the window of tolerance still requires bus services to depart from timing points up to 1 minute early and 5 minutes late. The punctuality target is also the same – 95% of your registered services need to operate within this window of tolerance.
Could not remember email address, password and username for tumblr - so unable to use. Not the best of websites anyway - a closed garden and not the best to search or use. Given the service up as a bad job.
National Express (NX) has terminated all its contracts with Nottingham-based YourBus, which was one of the largest contractors. YourBus has put all 35 of its Volvo B9R Caetano Levante coaches up for sale.
“The relationship with NX has been difficult for over two years. We have had continuous problems with vehicles that NX specified, and believe the expectations they put on operators and drivers are demanding and unrealistic.
Mr Dunn adds that, with the long-term decline of the UK coach and bus industry, it prompted the firm’s move to buy two businesses in Australia which “opposite to the UK has seen year-on-year growth.”