Muller was born to a working class family in New York City in 1890.
His father, Hermann Sr., had taken over the family metalworks shop abandoning a nascent career in law, when his own father, a German immigrant, died.
Hermann Sr. had strong interests in science, socialism, and emancipatory politics. Despite his unexpected death in 1900 when his son was only 9 years old, he was able to pass these interests onto his young son. Hermann considered his father instrumental in inspiring him to be a scientist, as he wrote in his autobiographical notes.
Growing up, he embraced a wide array of scientific interests from bug collecting to stargazing. Newspaper clippings in his childhood journal, indicate the breadth of his early scientific and socio-political interests. Meanwhile his mother Frances, of English and Sephardic Jewish descent, and a school teacher, encouraged Hermann with his studies.