Brown won a special election in January of last year to fill out Kennedy's unexpired term, following the Democratic senator's death in August of 2009.
Warren began her campaign Wednesday morning by meeting with commuters in Boston. By the end of the first day, she was expected to travel to several Massachusetts cities and towns in the central and western part of the state.
Warren was President Obama's choice to head up a new federal consumer protection agency, in light of the Wall St. financial crisis three years ago. However, strong Republican opposition caused her to step away.
"There's been a lot of very powerful interests who have tried to shut me down, squeeze me, push me sideways and so far it just hasn't worked," Warren said. "I'm willing to throw my body in front of a bus to try to stop bad ideas that are going to be harmful to the middle class."
She is now part of a seven-person Democratic primary field for the Massachusetts Senate seat. Some observers are looking ahead to the possibility of a Warren-Brown matchup in next year's general election.