As a child, his family moved to Dresden on an invitation by the court chapel to his father, an oboist.
Kummer, initially an oboist, took an interest in the violoncello and studied with notable performers Friedrich Dotzauer and Bernhard Romberg.
In the same year Carl Maria von Weber appointed Kummer as a violoncellist at the Royal Opera House.
[2] Kummer became an acclaimed performer and in 1850 he was appointed as the principal violoncellist at the court chapel after Dotzauer retired.
In 1839 Kummer wrote a method, Violoncelloschule für den ersten Unterricht (Violoncello School for Preliminary Instruction), Op.