WASHINGTON—The share of Americans getting married has fallen to its lowest level on record, according to government figures released Wednesday that reflect how economic insecurity and changing norms are eroding the institution.

The U.S. marriage rate fell 6% in 2018, with 6.5 new unions formed for every 1,000 people, according to a report by the National Center for Health Statistics. That was the lowest rate since the federal government began keeping data in 1867, said Sally Curtin, a statistician at the center and lead author...