The injury will likely not require surgery, the Boston Herald reported.
Coach Bill Belichick said Harrison will miss Sunday's game against the New York Jets.
"We all hope he'll be back out there soon," Belichick said.
Shoulder blade injuries can take anywhere from two to 12 weeks to heal, depending on the location of the break, former Red Sox team doctor Bill Morgan told the newspaper. The bone, also known as the scapula, connects the humerus (upper arm bone) to the collar bone.
Harrison missed a significant portion of last season after landing on the injured reserve list with a knee injury.
Harrison, who turns 34 in December, has 44 tackles, a sack and one interception through eight games so far this year for the 6-2 Patriots.
Notable deaths of 2014 [PHOTOS]