Mike Pence said in a statement Sunday that Bowen died at 6:18 p.m. Saturday at the Catherine Kasper Life Center in Donaldson, the South Bend Tribune reported.
"Gov. Otis R. Bowen's contributions to the life of this state and nation are incalculable, and I mark his passing with a sense of personal loss," Pence said.
Bowen, a Republican, was Indiana's governor from 1973 to 1981 and led the U.S. Department of Health and Human Services from 1985 to 1989.
Bowen, who worked as a doctor for 25 years, also served as a captain in the U.S. Army Medical Corps during World War II.
WSBT-TV, South Bend, first entered electoral politics in 1952 when he was elected Marshall County coroner. The TV station said he was the first Indiana governor to ever be elected to two consecutive terms.
As Health and Human Services secretary, Bowen took charge of the federal government's effort to stop the spread of AIDS after the Reagan administration was criticized by activists for a slow initial response, WSBT-TV said.
"All of his professional career as a legislator, as a governor and leader of arguably what was the largest department in federal government -- it was all about being in the best interest of people he was serving," former Gov. Joe Kernan said.
Pence directed flags at state buildings across Indiana be flown at half-staff through Saturday to honor Bowen.