McMahon beat out former Congressman Rob Simmons and Fairfield County money manager Peter Schiff for the Republican nomination on Friday night.
Simmons, a Vietnam veteran, said Friday that he would force a party primary in August. He received enough votes at the convention to do so.
The winner will face state Attorney General Richard Blumenthal in November. Blumanthal received the Democratic party's endorsement for the Senate seat earlier Friday.
McMahon has acknowledged that she provided information for news reports that Blumenthal had distorted his record of military service during the Vietnam War.