Danielle Burke allegedly sent the vile threats to Jasmine Middleton last year.
Burke married Katie’s attacker Stefan Sylvestre in December 2017, while he was still behind bars.
The 30-year-old was released from prison in October after serving nine years for throwing sulphuric acid into Katie’s face in 2008.
Burke previously told friends she did not care about her new hubby’s criminal past and went ahead with marrying the sick attacker over the phone in an Islamic ceremony.
The convicted acid attacker was not at the ceremony, instead reportedly giving his consent for a relative to stand in for him.
In the social media messages allegedly sent last year, Burke used her husband’s past to threaten the fellow mum, saying: “You know what my husband was in jail 4… I will get him to burn your face off you white b****.. do you think he wont touch you for me.
“I’ll get him to melt your bfs face off.”
There is no suggestion Sylvestre was aware of the threat.
The alleged victim, who claims she was driven out of London over the abuse, said she was left terrified after the threats were sent.
She claimed Burke had slept with the father of her children several years ago, with the pair never making up.
She said: “It upsets me on a day to day basis, it breaks my heart.
“I have to take medication on a daily basis because of everything I have gone through.”
A Met Police spokesman said: “On 19 December 2018 the Metropolitan Police received an allegation of malicious communication from a woman relating to message posted via social media.
“Officers spoke to a woman aged in her 30s and issued her with a harassment warning. She was not arrested.
“Both parties have been informed of the action taken by police.”
The model and mum of two was left with permanent scars on her face and blindness in one eye after she was attacked in 2008.
In her autobiography, Katie wrote about the terrifying moment she heard one of the thugs was seeking to be released.
She wrote: “The two of them had taken so much from me, and now this man’s punishment might soon be over.
“I thought: ‘I’m the one with the life sentence. Not him. He can change his identity, change his name, get a new job, a partner, move on, but I can’t.
“I can’t pretend it didn’t happen because it’s all over my face’.”
In November, Daily Star Online revealed how her ex-boyfriend and rapist has been handed almost £200,000 of taxpayer’s cash as legal aid.
Thug Daniel Lynch, 42, raped the Strictly Come Dancing star, 35, before ordering his friend Stefan Sylvestre to throw acid in her face, leaving her with horrific injuries.