The drummer co-founded the band in New York in 1974, along with singer Joey Ramone, bassist DeeDee and guitarist Johnny Ramone.
All four band members had different last names, but took the common name Ramone.
While the band never enjoyed mainstream success, they went on to inspire future generations of musicians and were inducted into the Rock and Roll Hall of Fame in 2002.
Tommy Ramone was born in Budapest in Hungary, but moved to the US as a child and grew up in New York.
Dave Frey, who works for Ramones Productions and Silent Partner Management, says Ramone's wife called to tell him that he passed away on Friday.