The letter, published on her Twitter account, ended with the words “count your days, we are going to take care of you.”
It also made several insulting references to her being African and how “she shouldn't be meddling in the life of the French”
Laetitia Avia, from Macron's Republique En Marche (Republic On The Move) party, said she had filed a complaint with police in Paris.
“I have never been attacked with such racism. And I've been threatened with death. We cannot let this happen,” the MP, whose family are of Togolese origin, told AFP.
She later told French TV that she was the victim of racist abuse on an almost daily basis but never had she been sent “words of such violence that are unrelated to her political commitment”.
Interior Minister Gerard Collomb said on Twitter he was “outraged by the hateful racist attack”.
It comes days after the announcement that a mixed-race teenager was the to play national heroine Joan of Arc for the first time in the French city of Orleans prompted a torrent of racist abuse online.
The 17-year-old, whose father is from Benin and whose mother is Polish, is set to ride horseback through the central city dressed in armour for an annual spring celebration dating back nearly six centuries.