Feldman was born in Potomac, Maryland. His father, Robert, runs an ad agency and his maternal aunt is chef Susan Feniger. Feldman was raised in his father's Jewish faith, attending Conservative and Orthodox denominations. He was involved in camp and school theater from the age of six, and attended Winston Churchill High School in Potomac. He worked as a camp counsellor in the theater and taught a videography class for several summers in Bethesda. He attended Ithaca College in New York, where he received a bachelor of fine arts in acting. After graduating, he moved to New York City, where he performed on Broadway and eventually moved to Los Angeles to act in film and television.
Feldman lives in Los Angeles, California, and is co-owner of a wine label called Angelica Cellars. In 2012, Feldman became engaged to Michelle Mulitz. They were married on October 12, 2013, at Smokey Glen Farm in Gaithersburg, Maryland. On October 24, 2017, the couple had their first child, Charlie.
He has done stage acting, including the Broadway play The Graduate along with Alicia Silverstone and Kathleen Turner. He also played a leading character in The Perfect Man and portrayed Fran Drescher's son on the television series Living with Fran.
From 2009 to 2011, he was a regular on the television series Drop Dead Diva in the role of guardian angel Fred. Feldman left the series at the start of the fourth season, although he made occasional appearances. In April 2012, he joined the cast of AMC's Mad Men as a regular, playing the character Michael Ginsberg. In 2014, he joined the cast of Silicon Valley as recurring character Ron LaFlamme, Pied Piper's young, laid-back but competent outside counsel. Also in 2014, he starred in A to Z as main character Andrew Lofland.
He directed his first Superstore episode "Lottery".