Last year the EIS union commissioned research looking at workload and stress. It found that on average, teachers were working more than 11 additional hours a week, unpaid, on top of their contractual hours.
A spokeswoman for the EIS said that "soaring" levels of stress and stress-related illness were a very serious concern.
"The Scottish government and local authorities, as the employers of teachers, must act in line with their duty of care to ensure that the current crippling workload burden on teachers is lightened."
Councillor Joan Griffiths, Edinburgh City Council's education, children and families convener, said she was "saddened" by the absence figures.
"The health and wellbeing of the over 3,000 teachers employed by the council is incredibly important to us," she said.
She said a range of support and resources were available to help, and that teachers who have concerns about their workload or mental health are encouraged to raise this with their line manager.
Angus Council said it recognised the challenges of the teaching profession and had a range of measures in place to support staff affected by stress.
A Scottish government spokesperson said it had allocated more than £2m in recent years to specifically support the wellbeing of the education workforce.
"Scotland continues to have the best-paid teachers and the lowest pupil-teacher ratio in the UK.
"We are also determined to increase teacher numbers in schools. That is why we are providing local authorities £186.5m this year as part of an agreement with Cosla to restore teacher numbers to 2023 levels, as well as freezing learning hours and making meaningful progress on reducing class contact time."
The spokesperson added: "Local authorities are responsible for the recruitment and deployment of teachers and headteachers."