Pudi was born in Chicago, Illinois, the son of Teresa, a programmer and analyst, and Abraham Pudi. His father is Indian, and his mother is Polish (born in Pokośno, Poland, to Marianna (Organek) and Boleslaw Komendant).
He studied dance in Chicago and attended Marquette University in Milwaukee, Wisconsin, graduating with a degree in Communication and Theatre in 2001.
Pudi is married to Bridget Showalter. They met while attending Marquette University their freshman year.Their twins, James Timothy Pudi and Fiona Leigh Pudi, were born on January 12, 2012. He is a runner, and has completed several marathons.
In 2009, Danny auditioned for and was eventually offered the role of Abed Nadir on "Community".