Reared in Indiana and Florida, Leininger attended Indiana University in Indianapolis, from which he received a Bachelor of Arts in 1965 and an M.D. in 1969. Following a two-year internship at the Leonard M. Miller School of Medicine at the University of Miami in Coral Gables, Florida, he completed post-graduate courses at the Center for Disease Control in Atlanta, Georgia, Brooke Army Medical Center in San Antonio, Walter Reed Army Institute of Research in Washington, D.C., and Fort Sam Houston in San Antonio, where he also lectured. He later settled in San Antonio and taught at the University of Texas Health Science Center from 1972-1973.

Married in 1976, Leininger and his wife, Cecelia, have four children and five grandchildren.

Leininger founded Texans for Justice in 1988, the Texas Public Policy Foundation in 1989, and has been involved with Texans for Governmental Integrity. He supported Thomas R. Phillips' campaign for Chief Justice of the Texas Supreme Court and has made significant donations to George W. Bush (while governor of Texas), former Governor Rick Perry, and the state Republican Party.

His other Business ventures include the private venture investment firm MedCare Investment Funds in 1991, the co-founding of ATX Technologies in 1994 (later serving on its board of directors), and co-founding the Renal Care Group in 1995. He has served as Director for the Emergency Department of the Baptist Health System in San Antonio (1975-1986) and on the board of Directors for Texas Commerce Bank (1985-1991). He currently sits on the boards of BioNumerik Pharmaceuticals and Spurs Sports & Entertainment.

In addition to political contributions, Leininger supports a range of charitable initiatives in areas including education, humanitarian aid, and scientific research. In 1997, he reportedly donated $1.5 million to Vanderbilt University, $2.5 million to Vision Forum, $3 million to the University of Miami, and $300,000 for diabetes research to the University of Texas Medical Center. Other recipients include Boy Scouts of America, Habitat for Humanity, the American Red Cross, the Mental Health Association, the Young Men's Christian Association, The Miracle Foundation, along with orphanages in India, Romania, Central America, Haiti, Ukraine, Russia, Myanmar, Thailand, and thirteen countries in Africa.

On the local level, Leininger's political action committees were involved in the narrow victory of Hispanic Republican Nathan Macias to the Texas House of Representatives in 2006. Macias unseated the more moderate lawmaker Carter Casteel of New Braunfels in the Republican primary for House District 73. However, Macias was himself narrowly upset in the 2008 primary by the more moderate Doug Miller, who still holds the Comal County seat just north of San Antonio.

He is a member of the American Medical Association, the Texas Medical Association, and the Institute of American Entrepreneurs. In 2007, he was inducted into the Texas Business Hall of Fame.