The forward fears for his wife Rebekah's safety after saying she had been cut up while driving with their children in the aftermath of ex-boss Ranieri's exit.
Vardy had been named as one of the players who allegedly met with the club's owners before Ranieri was sacked by the Premier League champions last month.
The striker, Marc Albrighton, Kasper Schmeichel and Wes Morgan all denied the claims they spoke to the Thai owners following their 2-1 Champions League defeat in Seville.
Ranieri, who guided Leicester to a shock title last season, was dismissed 24 hours later.
But Vardy - who has linked up with the England squad for games against Germany and Lithuania this week - conceded his denials have not stopped some fans targeting him and his family.
He said: "I read one story that said it (the meeting) was straight after the Sevilla game. It said I was personally involved in a meeting when I was actually sat in anti-doping for three hours. A few of you (media) waited around for an interview after.
"Then of course the story is out there and people pick it up and jump on it and you're getting death threats about your family, kids, everything.
"On social media, you name it - walking down the street. To be honest I get them every week.
"Football fans don't seem to like me. I just get on with it but when people are trying to cut your missus up while she's driving along, with the kids in the back of the car, it's not the best. It's happened plenty of times.
"It is terrifying. All that can happen is they get banned on Twitter. People get cut up but if there's no cameras you're screwed."