Blackburn, before observing the moment of silence for the victims, stated, "Let's take a moment and remember those who lost their lives in Pittsburgh and express our gratitude for the law enforcement who responded so beautifully".
To drown out the protesters' shouts, Blackburn supporters chanted "USA".
"If you are a red-state Democrat, this was a defining moment in your political career", Graham said.
The protester and at least nine others, including Black Lives Matter activists, were quickly removed from the rally in Davidson County, according to reports.
"We know they we're yelling "impeach Trump" among other things", Blackburn said.
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The favorability of President Donald Trump might be the difference for Rep. Marsha Blackburn, R-Tenn., in her bid for the Senate, as she leads Democrat Phil Bredesen by 8 points in the latest Emerson College poll. "And if you went with the mob, I think you are going to pay a price".
After the rally, Blackburn released a statement: "This Sunday afternoon, the liberal angry mob made it clear they are active in Tennessee and will stop at nothing to disrupt civil political discourse".
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Alyssa Hansen, Mr. Bredesen's campaign spokeswoman, called the incident a "shame". "They punched. They resisted law enforcement, and they interrupted a moment of silence for the victims in Pittsburgh". "Phil Bredesen is their leader and their behavior is despicable".
"This is not what this election is about and it is time to get back to bringing attention to fixing problems for the people of Tennessee", the statement read.
The Tennessee Democratic Party said it had nothing to do with the protesters at Sunday's event.