Candidates will have a tight window — about four weeks — to gather the required 10,000 signatures to get their names on the primary election ballot.
The general election is scheduled for June 25.
The winner of the special election will have to face voters again in November 2014, when Kerry’s six-year term would have expired.
Patrick this week named William “Mo” Cowan, a former top aide, to fill Kerry’s seat on an interim basis until the election.
Associated Press reporter Steve LeBlanc contributed to this report.