John Matthew Zwach Sr. (February 8, 1907 – November 11, 1990) was an American farmer, rural school teacher, and politician.

Zwach was born in Gales Township, Redwood County, Minnesota, the son of Austrian immigrants.

He worked as a school teacher and superintendent for fourteen years and was also an active farmer.

He was a member of the Minnesota Senate from 1946 to 1966 and was the majority leader from 1959 to 1966, leading the Conservative Caucus in the nonpartisan body.

His daughter, Barb Sykora, served in the Minnesota House of Representatives from 1995 to 2007.