Frenkel was born in Kiev, Ukraine. He was originally taught violin by his father, and later studied classical violin at the Kiev Conservatory under Yakob Magaziner . During the Second World War he was evacuated to Orenburg, where he studied at the Orenburg Zenitnoe Uchilishche, and played the violin in the orchestra of the Avrora Cinema. After the war he lived in Moscow, where he wrote orchestral arrangements and played the violin in various restaurants of the city.
He began composing songs in the 1960s. His first was the song Gody ('The Years'), written to lyrics by Mark Lisianski. During his later career he worked in collaboration with many prominent Soviet musicians, including Mikhail Tanich, Igor Shaferan, and the husband and wife team Konstantin Vanshenkin and Inna Goff. Thanks to Mark Bernes his song Zhuravli ('The Cranes', lyrics by Rasul Gamzatov) became a major hit. Frenkel gave concerts in which he performed his own music. During these concerts the audience would generally join in. His songs were included in the repertoire of many Soviet performers. He also appeared in the movie The Elusive Avengers, for which he composed a score.
Yan Frenkel died on August 5, 1989 in Riga (as foreshadowed in his song Avgust ('August') to the lyrics of Inna Goff). His wife Natalia died in the mid-1990s, but his daughter Nina has lived in Italy since the 1980s. His grandson Ian Frenkel is a musician (pianist and arranger) in the United States Coast Guard Band .
As reported by composer's fan site, members of Soviet ruling bureaucracy orchestrated a campaign against 'The Cranes', citing the song's religious undertones. The case was elevated all the way to the Soviet leader Leonid Brezhnev, who decreed "acceptable to perform, but not too often" .