Al Baldasaro, a New Hampshire state representative, told radio host Jeff Kuhner Tuesday that Clinton "should be put in the firing line and shot for treason."
"The U.S. Secret Service is aware of this matter and will conduct the appropriate investigation," said Shawn L. Holtzclaw, a spokesman for the Secret Service.
Trump spokeswoman Hope Hicks told CNN the campaign "does not agree with those statements."
She declined to characterize Baldasaro's role with the campaign or whether he would continue to travel with Trump on occasion.
Baldasaro, who serves as an informal adviser to Trump on veterans issues, has been one of Trump's most prominent supporters on the campaign trail, frequently introducing the candidate at events in New Hampshire. He has also traveled with the campaign to events around the country.
Baldasaro spoke during a news conference earlier this year after Trump invited him to the podium while fending off criticism about his lack of transparency in doling out funds raised for veterans charities.
Clinton's campaign communications director responded strongly.
"Donald Trump's overtaking of the Republican Party -- and his constant escalation of outrageous rhetoric -- is in danger of mainstreaming the kind of hatred that has long been relegated to the fringes of American politics where it belongs," Jennifer Palmieri said. "This week at the Republican convention, we've seen the clearest embodiment yet of this dangerous phenomenon."
Arkansas Sen. Tom Cotton on Wednesday objected to Baldasaro's comments.
"That's not keeping with the best traditions of American politics. We have opponents. We have adversaries. We don't have enemies in American politics so I can't agree with that kind of rhetoric," Cotton, a former U.S. army infantry officer, told CNN's Jake Tapper on "The Lead." "That kind of rhetoric has no place in our politics."
While Cotton acknowledged "geniune and serious concerns" about Clinton's conduct during the Benghazi attack, the junior Arkansas senator said the American people would judge the Democratic Party's presumptive nominee.
"I think her extremely careless handling of classified information, to use FBI director Jim Comey's term, disqualifies her from being president, but I think the way to handle that is to let the American people make the choice and render their verdict this November," Cotton said.
Baldasaro called Clinton a disgrace for lying to the families of the four men killed in Libya and for her use of private email servers while secretary of state.
"This whole thing disgusts me. Hillary Clinton should be put in the firing line and shot for treason," he said in the interview, which was first reported by BuzzFeed