Ranieri led Leicester to a historic Premier League title last term, but the Italian got the sack when the champion failed to replicate that form this campaign.
Reports surfaced that Vardy was among the players who had asked for Ranieri's departure and - even though the England international quickly dismissed such claims - angry fans targeted him and his family.
"The story is out there, then people pick it up and jump on it and you are getting death threats about your family, kids, everything," Vardy said.
"The threats were on social media, walking down the street, you name it.
"I try to get on with it but when people are trying to cut your missus up while she is driving along with the kids in the back of the car it is not the best. It has happened plenty of times. It is terrifying."
Vardy remains adamant, however, that he had nothing to do with Ranieri's sacking.
"The stories were quite hurtful. A lot of false accusations were being thrown out there and there is nothing us, as players, could do about it," he said.
"Apparently the meeting that got him sacked, I read one story that said it 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. Absolute shambles."