The airport said in a statement on Twitter that the incident occurred at 9.39am on Saturday and the pilot and two passengers on board needed emergency care.
It said its runway would remain closed “until further notice” while an investigation is carried out.
The airport said: “We can confirm an incident occurred today involving a light aircraft at 9.39am. A pilot and two passengers were onboard and have been taken to hospital.
“Our runway will remain closed until further notice while a thorough investigation is carried out.
“We would like to thank the emergency services (and) on-site staff for their quick response.”
In a message to passengers due to travel on outbound Ryanair flights, it said: “Arrangements have been made for all passengers to be coached to Newcastle Airport where the flight will depart.
“Please note, you must check-in for your flight at Teesside.
“We’d like to thank you for your patience and cooperation.”
A spokeswoman for County Durham and Darlington Fire and Rescue Service said that two fire engines had attended the scene but the incident was now closed.
She said that the airport’s own fire and rescue unit had been part of the response, and confirmed there had been three casualties.
Tees Valley mayor Ben Houchen tweeted: “Thoughts and prayers are with the three people onboard at the time of the incident and their families.
“At this time I want to thank the incredible response by the airport fire service and the immediate response of local emergency services to the incident.”
