Romo is scheduled to undergo a Mumford procedure, which involves shaving a portion of the clavicle to relieve pressure against the shoulder.
Last week, Romo was said to be considering the insertion of a plate into the collarbone. But the results of a CT scan on Wednesday apparently made him change his mind.
The 35-year-old Romo is expected to be ready for Organized Team Activities in May after six to eight weeks of recovery.
Last season, Romo was plagued by collarbone issues, breaking it twice. The first time was Sept. 20 against the Philadelphia Eagles and the second time came on Thanksgiving Day in a loss to the Carolina Panthers that ended his 2015 season.
Romo's collarbone was also broken in 2010.
In four starts last year, Romo finished with five touchdown passes and seven interceptions.