Martha Robinson Rivers was born in Charleston, South Carolina, the daughter of John Minott and Martha Elizabeth Robinson Rivers. She was educated at Ashley Hall in Charleston. She graduated from Vassar College with a Bachelor of Arts in history in 1957.
She married E. Bronson Ingram II, the son of Business magnate Orrin Henry Ingram, Sr., on October 4, 1958, at St. Philip's Episcopal Church in Charleston, South Carolina. They had three sons: Orrin H. Ingram II, John R. Ingram, and David B. Ingram, and a daughter, Robin Ingram Patton.
Ingram was honored by Business Week as the 50th most generous philanthropist for her donations between the years 2000 and 2004. In 2006 she was honored by the Community Foundation of Middle Tennessee as the 2006 recipient of the 13th Annual Joe Kraft Humanitarian Award for her philanthropic efforts. She received the Eli & Edythe Broad Award for Philanthropy in the Arts.
Ingram was a co-founder of the Schermerhorn Symphony Center which opened in 2005. She formerly served as Chairman of the Board of Trust of Vanderbilt University in Nashville. The Vanderbilt Blair School of Music has been the recipient of $300 million of Ingram company stock.
In 2015, Ingram donated to Democratic candidate Megan Barry's campaign to become the new Mayor of Nashville.