Liam Hanson told the woman: "I am going to kill you. If you walk past my house, you are dead".
Southern Derbyshire Magistrates' Court was told that Hanson began swearing and shouting at the mum when she arrived at the school to collect her child.
She was talking to another mum when Hanson first started shouting abuse at her, only stopping when a school governor intervened.
District Judge Joanne Alderson told the court: "This was an unprovoked verbal attack involving threats and foul language, aggravated by the fact it took place at a primary school where small children were in sight and hearing of what was going on."
"A school governor said she felt she had to go and approach him to intervene.
"There were other parents and primary school-age children present. The victim was visibly shaken and exceptionally upset."
Hanson's lawyer, Stephen Cooper, said there was 'history' between his client and the woman, and that she had previously received a court order to stay away from his partner.
"Since then, there have been incidents where this lady has approached him," he said. "He has not reacted. It is an important factor that there is more to it. There are two sides to this.
"He clearly chose the wrong way to react on the day in question."
When questioned by police, Hanson accepted he had been 'swearing on numerous occasions' and that the woman may have felt 'threatened' by his behaviour, but he denied he made threats to kill her.
The victim said she had been left feeling 'intimidated and threatened' by the incident and was now 'scared' to walk on her own.
Hanson was sentenced to 12 weeks in prison.