Claudia Webbe, a former Labour MP for Leicester East who is now independent, was convicted of one charge of harassment last month.
Westminster Magistrates’ Court heard she made several calls over two years while it was claimed she threatened the woman with acid.
Webbe was handed a 10-week sentence, suspended for two years, on Thursday.
The 56-year-old made 16 calls to Michelle Merritt, a long-term friend of Webbe’s partner Lester Thomas, between September 2018 and April last year in a campaign of harassment borne out of jealousy, the court heard.
The court was told on one occasion she made an “angry” call, used a derogatory term and added: “You should be acid.”
Chief magistrate Paul Goldspring, sentencing, said: “I have no doubt that, when not overtaken by jealousy and rage, you are a hard-working, upstanding member of Parliament and of society.
“[But] the level of harassment and the threats you made cannot be excused.”
He added Webbe “showed little remorse or contrition” and would have been jailed immediately were it not for her previous good character.
The sentence means Webbe will face a recall petition, which could trigger a by-election if at least 10% of her constituents support it.
However, the process is pending any appeal by Webbe against her conviction, an avenue she said she would pursue.
In a statement, Webbe said: “I am very disappointed by the decision of the magistrate and want to strongly reiterate that I am innocent.
“I am lodging an appeal and despite today’s sentence, I fully expect the appeal to be granted and that, ultimately, it will be successful.”
She will remain the MP for Leicester East, but as an independent member of Parliament, as has been the case since she was suspended by the party last year after she was charged then subsequently expelled last month after being found guilty of harassment.
Webbe, 56, who was elected in 2019 after Keith Vaz stood down following a rent boy and drugs scandal, had been suspended by the party after she was charged with harassment.
Her expulsion now means she will not be able to stand as the Labour candidate in the next General Election, and she would have a tough job beating whoever the Labour Party put forward for the seat.
There has been speculation that Keith Vaz could even return as a Labour candidate, despite the incident that led to his resignation and the more recent scandal over his “significant misconduct” in bullying a female House of Commons employee, who Mr Vaz compared to a prostitute.
There is a chance the next Leicester East MP could be chosen through a by-election before the next General Election comes around. It would need 10 per cent of the population of the constituency – about 12,000 people – to petition for it.
Webbe has already announced that she will be appealing against her harassment conviction and the petition could not begin until after the appeal process is done.
Webbe, of Islington, north London, was also ordered to carry out 200 hours of unpaid work and told to pay £3,128 in costs and surcharges.