NUT Cymru had responses from 17 of Wales' 22 local authorities to Freedom of Information requests.
The number of assaults average at eight per school day in Wales, which the union said was "a great concern".
It said they needed to be considered by schools, councils and the Welsh Government.
The Welsh Government has been asked to comment.
One teacher, who asked to remain anonymous, told BBC Wales he was punched by a teenage pupil as he tried to stop a fight in his classroom.
The teacher, who has more than 20 years experience in the classroom, has spent more than six months on sick leave.
"I was punched in the face, it was a really violent incident," he said.
"It was like an out of body experience. You think, is this really happening?
"I was in shock. Everything seemed to happen in slow motion."
NUT Cymru secretary David Evans said: "Clearly any incidents of physical or verbal assault by pupils towards teachers or any members of the school staff are unacceptable.
"The details of the FOI do not cover the severity of these assaults but of course we can only assume that they were notable enough to warrant school staff to feel the need to report them."
Pembrokeshire council recorded the highest number of incidents by far - 1,268 over three academic years.
Of these, 1,268 were physical and 77 verbal.
A spokesman said councils had varying approaches to the reporting of violent incidents and comparing figures from different areas could be misleading.
He said the council had been "particularly robust in improving its recording and logging of physical and verbal violence against staff in its schools in order to give a true picture of the situation".
The council said this ensured that the staff received the best possible support.
It added that many of the incidents took place in the authority's specialist education units rather than in its mainstream schools.
Union officials said the real number of attacks in Wales could be much higher.
NUT Cymru has also questioned how different local authorities recorded the incidents.
"It does beg the question why there isn't a more standard approach to monitoring which would help in terms of putting in place policies and training to reduce the impact it may have," Mr Evans added.
The union said assaults not only had an impact on individual teachers but disrupted the classroom environment.
Cardiff head teacher Jason Clark has faced verbal abuse from a pupil and even a physical assault by a parent.
He said these kind of events were rare and staff were trained to deal with them.
"You rely on your training, you go straight back to what you've been taught - provide a calm space so you can de-escalate the incident as soon as possible," he said.
"It's only later that you can start to reflect on the emotional struggle that child is going through and also how it makes you feel."
Welsh Conservative education spokesman Darren Millar AM said it was "very concerning to see such a high prevalence of unacceptable behaviour in our classrooms".
"We need more discipline in our schools, more support for teachers in managing unruly behaviour and targeted intervention to support pupils with behavioural problems," he said.
"It is clear from these figures that the current arrangements aren't working and that we need a Welsh Government strategy to tackle the roots of these problems once and for all."
Teachers and school staff in Wales have been the victims of more than 1,500 physical and verbal attacks by pupils every year, figures have shown.