After what Education Minister Benoit Hamon described as an "appalling" crime, the 47-year-old assailant fled to her home but was quickly detained by police.
The attack on the 34-year-old teacher took place around 9 am (0700 GMT) as classes began on the last day of term at Albi's Edouard Herriot primary school, which is attended by 284 students aged
from three to 11.
Officials said the mother showed up in the classroom with a knife and stabbed the teacher, Fabienne Terral-Calmes, a mother of two young girls, in front of her horrified pupils.
The teacher died at the scene while being treated by emergency services.
The assailant's young daughter had been enrolled at the school for about a month-and-a-half, officials said, but it was unclear if the girl was in the classroom at the time of the stabbing.
"This is an appalling act, a murder, a murder of a teacher in her classroom in front of her students, by a woman who… seems to suffer from significant psychiatric problems," Hamon said after arriving in Albi.
"I want to pay hommage to the memory of Fabienne Terral-Calmes. She was 34 years old, a school teacher and mother to two little girls, Romane and Adele," Hamon said.
"They have lost their mother and the national education system has lost a wonderful teacher."
The head of the local parents' association, Sandrine Soliman, said she had spoken to the school and been told "there was no particular problem between the teacher and this woman."
- Better protection for schools -
Touring the school, Hamon said more needed to be done to protect institutions and teachers.
"This was an isolated act of course but… we must work to ensure that in the future schools are better protected," he said.
President Francois Hollande offered the government's full support to those involved.
"All state services will be mobilised to take care of these children and the staff who witnessed this awful tragedy," he said in a statement.
The incident comes amid concerns in France over assaults on teachers, with a study released on Thursday saying that education workers were twice as likely to be threatened and insulted than people in other professions.
The study by the INSEE state statistics agency found that 12 percent of education workers suffered threats and verbal abuse.
Only 0.6 percent of education workers reported suffering physical attacks however.
Another study released in April said nearly half of primary school principals reported being verbally or physically abused.
Of 4,000 principals questioned in the study, 49 percent said they had suffered from harassment, threats or insults in the 2012-13 school year.
It is still extremely rare for teachers in France to be killed in connection with their work, with only four known cases in the last 30 years.
The last was in 1995, when 51-year-old English teacher Michel Antoine was beaten to death in the southwestern town of Dax by two students, one of whom had just flunked his exams.
The two were later both sentenced to 10 years in prison.
There have been more cases of simple assaults on teachers, in several cases involving parents.
In October 2012 a father was sentenced to three years in prison, with 18 months suspended, for having struck a Lyon gym teacher several times with a truncheon after entering the school gymnasium to complain of his daughter being excluded from a basketball game.