Ms Rudd quit this month as work and pensions secretary and resigned from the Tory Party after accusing the PM of purging moderates from the Government benches.
She told the Evening Standard No.10's recent words were seen to encourage a "more aggressive approach".
“The sort of language I'm afraid we've seen more and more of coming out from Number 10 does incite violence," she said.
"It's the sort of language people think legitimises a more aggressive approach and sometimes violence."
Ms Rudd told the Evening Standard she had been "disappointed and stunned" when Mr Johnson dismissed "genuine fear that a lot of women have" following the 2016 murder of Mrs Cox.
She said the "casual approach to safety of MPs and their staff is immoral".
Ms Rudd said Mr Johnson's rhetoric was "reminiscent" of US president Donald Trump leading chants of "lock her up" in the 2016 presidential race, which referred to rival Hillary Clinton.
Labour MP Paula Sherriff confronted the PM in the Commons on Wednesday, telling him online abusers used identical terms to Mr Johnson, including talking about "surrender act, betrayal, traitor".
But speaking during a hospital visit in 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."
The PM's chief adviser Dominic Cummings said during an event on Thursday night the anger directed against politicians was "not surprising".