Varshavskaia was born in 1925 in the village of Mikhailovka, near Poltava, Ukraine to a family of Jewish musicians. Her parents were ardent Communists, and gave their children Communist names: their son was named Kim (the first letters of the Russian abbreviation of "Communist International of Youth"). Their daughter, who was younger than Kim, was named Lenina, after the Soviet Communist leader. Their family moved to Moscow, where Lenina graduated from the Central Music School of the Moscow Conservatory and entered the Gnessin State Musical College to study the cello.
As an outstanding student at the Gnessin school, Varshavskaia was entitled to be evacuated from Moscow. Instead, without informing her parents, she left the train on which she and her parents were going to be evacuated and volunteered to be a nurse. The note she left to her father said: "Father! A different music is needed now." She feared that her parents would look for her and eventually return her home as a minor (she was only 16 years old at that time) so she changed her name from Lenina to Elena. As Elena, she was drafted into the Red Army, but because she was a minor, she was not sent to the front but left in Moscow as a nurse at a military hospital. Only in 1943 was Varshavskaia sent to the frontlines.
In the summer of 1943, while serving as a nurse near Orel, southern Russia, she managed to capture two German saboteurs. As a frontline nurse, she evacuated dozens of wounded soldiers from the battlefield, thus saving their lives. In September 1944, in the course of the Soviet offensive to take Tallinn, Estonia, she was killed during an enemy air raid on the truck column with which she was going to enter the city. When a German Messerschmidt machine-gunned the column, the vehicle in which she was riding overturned and Elena was crushed to death. She was buried in Tallinn, at the site of the memorial to the Soviet soldiers.
Varshavskaia had been awarded the Order of the Patriotic War, 1st class, and the Order of the Red Star.
Her brother Kim Varshavskii was killed in action in 1943.
In 2007, when the authorities of Estonia destroyed the memorial to the Soviet soldiers, Varshavskaia was reburied in Israel, in the cemetery on the Mount of Olives in Jerusalem.