Caws was born in New York City, the son of Peter James Caws and Mary Ann Caws. His parents divorced in 1987.
Caws' mother, a Distinguished Professor of Comparative Literature, English, and French at the Graduate Center at CUNY, lives in New York City. In 2007, his mother married Dr. Boyce Bennett. She was born and raised in Wilmington, North Carolina. Caws' maternal grandmother, Margaret Devereux Lippitt, was the daughter of painter Margaret Walthour Lippitt.
Caws' father, University Professor of Philosophy at George Washington University, lives in Washington, D.C.. His father married Nancy Breslin, M.D., M.F.A., a psychiatrist turned fine art photographer. He was born in Southall, Middlesex, now part of West London, England. Caws has a half sister from his father's second marriage named Elisabeth Breslin Caws.
Caws has an older sister, Hilary Caws-Elwitt. She is married to humorist and playwright, Jonathan Caws-Elwitt, who also writes erotica under the nom de plume, Jeremy Edwards. They formed the band The Silly Pillows together and live in Northampton, Massachusetts.
Matthew Caws' parents, both university professors, took sabbaticals in France—in Paris, and in the Vaucluse in Provence—which helped Matthew develop early skills in French.
When the family returned to New York City, his parents sent him to le Lycée Français de New York. There he joined The Cost of Living in 1982 or 1983, a band formed by a teacher, Patrick Thouron, and a few students, including Daniel Lorca, Stéphane Dehais, and Fabrice Griffoulière-Frère, initiating a long friendship and a promising collaboration.
The Cost of Living split up in 1990, after having released two records, played in venues such as the CBGB, and even having a video played on MTV, but Matthew and Daniel joined another band, Because Because Because, with two other musicians. This enterprise was short-lived and they soon split up, despite the recording of a demo, unreleased to this day, for the label Stickboy, which would later release Nada Surf's first single (7"), "The Plan/Telescope", in 1994.
Hilary, Matthew's elder sister, was a DJ for a campus radio. She helped develop and influence her younger brother's musical tastes, lending him records from her impressive collection and cassette tapes of her show. Matthew joined the project initiated by Hilary and her partner, Jonathan, The Silly Pillows, for a few collaborations.
He was also writing and editing for Guitar World, interviewing, among others, Oasis and Mick Jones.
In 2013, Caws and singer-songwriter Juliana Hatfield formed the new band Minor Alps. The duo's debut album, Get There, was released on October 29, 2013 on Barsuk Records.
Julie Gayet, alleged girlfriend of French president, Francois Hollande appears on the Minor Alps music video of their song "Waiting For You."
In 2016 he married Emily Bidwell. The couple has stated they will split their time between Caws' residence in Cambridge, England and New York.