Lynsey Haycock, 41, is believed to have died after suffering from complications following the accident at Forge Valley School, in Sheffield, South Yorkshire, last week.
A book of condolence will be available at the school for people to leave their tributes.
Dale Barrowclough, headteacher at Forge Valley, said: "Mrs Haycock was a much-loved and respected teacher whose dedication and hard work helped improve the life chances of all the pupils who were fortunate to have her as a teacher.
"We all came to know Mrs Haycock as a very warm-hearted person with a great sense of humour. Not only was she treasured by staff, she was much loved by the pupils at Forge Valley.
"As a community, we are devastated by this tragic death and our thoughts are with Mrs Haycock's family and friends during this very difficult time."
Former pupils and colleagues also paid their respects to Mrs Haycock on Facebook.
Helen Stokes wrote: "RIP Lynsey. Worked with her at a previous school. Much love to her family and friends."
While Kirsty Elizabeth Perry said: "RIP Lynsey (Miss Arnott as I knew her). My deepest sympathies to her family."
Adele Logan also said she had worked with Mrs Haycock. She wrote: "Dreadful news. Worked with her at Horizon. RIP, thoughts with her husband and children."
Aneela Shah added: "RIP, gone too soon. Was a true professional and lovely woman. Covered her class when doing supply."