Bill Schuette says he filed a brief this week in U.S. District Court in Detroit.
Monaghan's case is to be heard Thursday. The devout Roman Catholic says contraception is a "gravely immoral" practice. His lawsuit also lists as a plaintiff his Domino's Farms, an office park outside Ann Arbor.
He has sold most of his controlling stake in Domino's Pizza.
Monaghan offers health insurance that excludes contraception and abortion for employees. The new federal law requires employers to offer insurance including contraception coverage or risk fines.
Schuette said in a release Wednesday that the law "will force private sector job-providers across America to violate their conscience."