John Connolly, a former school teacher, would likely face an uphill fight if Menino, 70, seeks a sixth term in the office he has held since 1993. Both are Democrats.
Menino has not yet declared whether he will run again after a month-long hospitalization late last year related to a virus he contracted while on vacation in Italy.
Connolly, 39, said in a posting on his website that his focus as mayor would be improving the city's school system.
"Mayor Menino is a good man," Connolly said. "I've worked with him and I respect him immensely, but transforming our schools requires new ideas, new energy and a bold desire to break the status quo."
Incumbent mayors in Boston rarely lose re-election. Menino's predecessor, Raymond Flynn, stepped down when President Bill Clinton named him ambassador to the Vatican.
In the city's 2009 mayoral election, Menino's most serious challenge came from then-city councilor Michael Flaherty, who has since left politics and gone into private legal practice.
Should Menino not run again, a decision he does not have to make until May, Connolly's early entrance could give him an advantage against other rivals, said John Berg, professor of government at Suffolk University in Boston.
"It lets him get out there and get known as a guy who was brave enough to challenge Menino, as opposed to just hanging back and waiting," Berg added. "If Menino drops out, he gets a leg up."
(Reporting By Scott Malone; Editing by Paul Thomasch, Nick Zieminski and Andre Grenon)