Grażyna Bacewicz was born in Łódź, Poland. Her father Wincenty Bacewicz identified as Lithuanian and also used the surname Bacevičius. He gave Grażyna her first piano and violin lessons. In 1932, she graduated from the Warsaw Conservatory, and received a stipend from Ignacy Jan Paderewski to continued her education at the École Normale de Musique in Paris. There she studied with Nadia Boulanger and André Touret. She returned briefly to Poland to teach in Łódź, but then went back to Paris in 1934 in order to study with violinist Carl Flesch.
In 1936, she became the principal violinist of the Polish Radio Orchestra, and took part in numerous events as a soloist, composer, and jury member. During World War II, she lived in Warsaw and gave underground concerts, premiering her own works at the time. Following the Warsaw Uprising near the end of the war, she and her family fled the destroyed city and temporarily settled in Lublin. She later became a professor at the State Conservatoire of Music in Łódź.