Margaret Georgiadou, who is thought to be from Huddersfield, set up the petition in February.
Today she said she would also be closing her Facebook account due to the barrage of messages.
“In the past 10 hours have had three death threats over the phone,” she wrote on Twitter.
“My Facebook account has been hacked and had a torrent of abuse on Facebook. Am closing my Facebook account.
“I am currently visiting Cyprus and last night I had three telephoned death threats. Who wants Brexit so much that they are prepared to kill for it?”
The former lecturer’s petition, which calls on the Government to revoke Article 50 in order to stay in the EU, was so overwhelmed with signatures it crashed the Parliament.uk website.
At one point, 2,000 people were signing every minute.
Speaking on LBC about her reasons behind setting up the petition, Ms Georgiadou said she felt remain voters were being “silenced and ignored”, adding that she could not believe how popular her petition had become.
“I was very annoyed that Remainers seemed to be silenced and ignored and no one seemed to be doing anything about it, so I thought I’d go for what I really want, which is to revoke Article 50 and stay in the EU,” she added.
Today, pro-Brexit 'go slow' protests have been taking place across the country by lobbying Leave supporters. Within 10 minutes, police had stopped a convoy in Yorkshire.