The 2014 Shrewsbury, Massachusetts, population is 35,583. There are 1,717 people per square mile (population density). The median age is 39. The US median is 37.2.61.28% of people in Shrewsbury, Massachusetts, are married.7.93% are divorced.The average household size is 2.69 people. 46.83% of people are married, with children. 9.45% have children, but are single.1.28% of people in Shrewsbury, Massachusetts, are married. 7.93% are divorced. The average household size is 2.69 people. 46.83% of people are married, with children. 9.45% have children, but are single.