The Dewsbury MP told ITV News the nature of the threats were so horrific the police will speak to her on Friday about the messages.
She repeatedly criticised Boris Johnson in the House of Commons earlier this week for repeating the term "Surrender Act" when describing legislation designed to stop a no-deal Brexit on October 31.
"I've received death threats, I've received rape threats, I've been shouted at in the streets, I've had abusive phone calls," Ms Sherriff told ITV News.
"And indeed, since I raised the issue in the House of Commons this week we've seen a significant escalation and I am waiting for the police to visit me this afternoon regarding some specific threats I've received in the past 24 hours."
Ms Sherriff was one of a number of MPs from across the political spectrum to speak out about the abuse she has received in recent months.
She added while she excepted her voting record or opinions to be questioned, she said debate in political risked descending into personal insults.
"I expect constructive criticism, I expect people to question me on my voting habits, of course I do," Ms Sherriff said.
"But there is never any excuse for threatening to kill, or harm, or rape. The abuse that is being sent at the moment is absolutely abhorrent, and some of that is being done in the name of our prime minister."
The prime minister has refused to dial down on the language he uses, saying it was important not to "impoverish political debate".
Speaking on a visit to Harlow, Essex, Mr Johnson said: "I think the threats against MPs and particularly female MPs are absolutely appalling and we're doing a lot of work to give MPs the security that they need.
"But then there's another question which is - can you use words like 'surrender' to describe a certain act or a certain bill?
"And, quite frankly, I think that you can and if you say that you can't then you're kind of impoverishing the language and impoverishing political debate because, after all, the use of that kind of metaphor has been going on for hundreds of years."