Zacharias Hackzell was one of the five children born to Anders Mårtensson Hackzell (1705–1757) and Anna Catharina Plantin (1663–1741), of which three were sons (one died at birth) and two were daughters.
Anders Hackzell died on February 13, 1757, two weeks before his son's sixth birthday.
Hackzell had at least three more children with his second wife: Sofia in 1787, Zackarias in 1791 and Olof in 1800.
At the time, Finland was still a part of the Realm of Sweden.
Five years after the death of Hackzell in 1809, Finland became an autonomous Grand Duchy of Russia (1809–1917).