Northamptonshire Police said the balloon came down in a field next to the B573 by Earls Barton, near Northampton, at around 7.30am on Sunday.
The woman, who was on board the balloon, was taken to Queen Elizabeth Hospital for treatment.
The Air Accidents Investigation Branch (AAIB) will investigate, police said.
A spokesman for the AAIB said: “We are aware of the incident and are making enquiries.”
A man who claimed on Facebook that he saw the incident said the balloon basket hit power cables near the field.
Steve Tee said: “The balloon seemed to struggle to gain the altitude. The balloon basket hit the power lines causing it to burst into flames.
“The balloon to rapidly deflate and plummet. I hope all involved are going to be ok.”