The airport says it hopes to be able to open on Monday (Sep 27) following the light aircraft crash which led to the pilot and two passengers being taken to hospital.
The Air Accident Investigation Branch is now carrying out an investigation into the incident.
A statement from the airport, which was posted on its website and social media, said: "Following an incident involving a light aircraft this morning, we will remain closed for the weekend so the Air Accident Investigation Branch can carry out a thorough investigation. We are hopeful the airport will reopen on Monday.
"As a result of this closure, Loganair will be contacting customers affected with details on how to claim a full refund or rebook an alternative date. They request that customers do not phone Loganair at this time.
"We apologise for any inconvenience caused and thank all of our passengers who have been very understanding today. All of our thoughts and prayers are with the three people onboard at the time of the incident and their families."
A number of flights were diverted to Newcastle Airport on Saturday.
Loganair also issued a statement, saying: "We regret to inform you that there has been an incident at Teesside Airport which has resulted in a runway closure today. We can confirm that at no time was a Loganair aircraft involved.
"We apologise for any inconvenience this may have caused to your travel plans but must stress that this out with our control and we will do our very best to assist you with making alternative arrangements."