Clark will face Republican Frank Addivinola Jr. in the general election to replace Markey, who won a special election in June for the U.S. Senate.
Clark had 31.6 percent of the vote while Middlesex County Sheriff Peter J. Koutoujian and state Rep. Carl M. Sciortino had 22 percent and 16.1 percent, respectively, in the Democratic primary, The Boston Globe reported.
President Barack Obama won the district north and west of Boston by more than 30 percentage points in the 2008 election, and Clark is expected to win Dec. 10, becoming in the fifth woman to represent Massachusetts in the U.S. House.
Addivinola, a businessman from Boston, which is not in the district, won 49.1 percent of the GOP primary vote.
Both candidates are lawyers.