Terrorist Ali Harbi Ali stabbed Sir David more than 20 times after tricking his way into a constituency surgery in Essex last year.
The Isis fanatic was given a whole-life sentence this week for murdering Sir David in a jihadist-inspired attack.
His conviction and sentencing has led to calls for greater protection for MP during their interactions with the public.
However, South Ribble Conservative Mrs Fletcher says it's not her safety but rather her colleagues’ she fears for.
"It is a big issue for my staff and their families. It has a knock on psychological affect.
"My staff are very fearful."
She says she is now conducting some constituency surgery meetings online and some in-person.
"I have been doing a bit on Zoom but I don't want to become that MP,” she said.
"I kind of accepted the risks of this job when I started.”
Sir David is the second MP to be murdered in recent years. In 2016, Labour MP Jo Cox was killed in Birstall, West Yorkshire, by right-wing extremists Thomas Mair.
He was also sentenced to a life imprisonment with a whole life order.
Mrs Fletcher, however, views the risks as part and parcel of her job as a constituency MP.
She added: "Yes, I am pragmatic, but I made my peace with it a long time ago as I want to be able to serve the people of South Ribble."
Neighbouring MP Sir Lindsay Hoyle, who represents Chorley and is the Speaker of the House of Commons, ordered a review of MPs’ security following Sir David’s murder.
An following Harbi Ali’s sentencing, he said: “The end of this trial and this distressing episode should strengthen our belief in the fundamental principle of democracy that Members and their staff must be able to perform their Parliamentary duties safely both on and off the Estate, and our resolve to ensure they can.”