President Donald Trump has questioned the neutrality of Mr Mueller, who was appointed to investigate Russian interference in the US election.
He has also blamed Attorney General Jeff Sessions for Mr Mueller's probe.
Mr Graham warned Mr Trump that firing Mr Mueller "would be the beginning of the end" of his presidency.
"Any effort to go after Mueller could be the beginning of the end of the Trump presidency unless Mueller did something wrong," Mr Graham told reporters on Thursday.
The Trump administration has sought to discredit Mr Mueller over his friendship with former FBI chief James Comey, who had been heading the inquiry until he was sacked by Mr Trump in May.
The president has also suggested Mr Mueller's team of lawyers could be biased as some had made campaign contributions to Democrats.
By Anthony Zurcher, BBC News, Washington
There's no telling if Lindsey Graham's legislation insulating the independent counsel Robert Mueller from Donald Trump's wrath will go anywhere. The South Carolina Republican has been known to occasionally wander from the Senate flock.
Still, this could be the first glimmers of bipartisan congressional efforts to construct a restraining barrier around the Trump presidency.
Already it appears likely a bill preventing Donald Trump from unilaterally loosening current Russia sanctions will wind up on the president's desk. Despite the administration's objections that this infringes on executive foreign policy prerogatives, hardly any members of Congress have voted against the legislation.
Now, amid concerns that Mr Trump may fire Attorney General Jeff Sessions as a way of getting at Mr Mueller, another set of handcuffs could be applied.
The White House appears to be girding for war against those investigating Russian meddling in the 2016 election and any connections to the Trump campaign. Chances are this more aggressive posture, including a presidential feud with Mr Sessions - who served in the US Senate for 20 years - will only make matters worse, however.
Like a person trapped in quicksand, the more the president struggles, the deeper he sinks.
Mr Mueller has not given any details of his investigation but US media have reported he is investigating Mr Trump for possible obstruction of justice, both in the firing of Mr Comey and whether Mr Trump tried to end an inquiry into sacked national security adviser Michael Flynn.
President Trump has repeatedly denied any collusion with Russia, calling it a "witch hunt".
The South Carolina Republican announced he was creating a measure aimed at protecting Mr Mueller by mandating that any special counsel appointed to investigate a president or his staff could not be fired "unless you have judicial review of the firing".
He added that Mr Trump was crossing a "red line" in his consideration to axe Mr Mueller, who was appointed by the Justice Department to lead the probe after Mr Comey was fired.
Mr Graham's warning comes as the president has repeatedly attacked Attorney General Jeff Sessions, who recused himself from the Russia inquiry after failing to disclose a meeting with the Kremlin's envoy during his confirmation hearing.
Mr Sessions, known for his hardline anti-immigration stance, was one of then-candidate Mr Trump's earliest supporters in Washington.
Earlier this week, Mr Trump said he was "disappointed" with Mr Sessions, tweeting that he had "taken a VERY weak position" on the investigation into Hillary Clinton's use of a private email server while she was secretary of state.
In an interview with the New York Times, the president expressed regret about appointing Mr Sessions, adding he "should have never recused himself".
Anthony Scaramucci, the president's new communications director, fuelled the fire on Tuesday by suggesting the attorney general's days could be numbered.
Mr Graham on Wednesday said "there will be holy hell to pay" if Mr Sessions is fired, warning that there would be "no confirmation for a new attorney general in 2017".
"This is not just a diversion, this is unnerving," he told reporters. "It's unfair to Jeff Sessions, he's a good man who deserves better, and some of the suggestions the president is making go way beyond what's acceptable."
US Senator Lindsey Graham has said he is drafting legislation to stop any attempt by the Trump administration to fire Russia investigator Bob Mueller.