Kardashev was a Russian physicist who, in the 1960s, proposed a framework for rating civilizations by their energy use.
Kardashev was Soviet (Russian-born), and the scale was proposed in 1964. However, he was an astronomer/astrophysicist, not specifically a 'physicist'.
Nikolai Kardashev was a Soviet radio astronomer born in Moscow in 1932. He introduced his civilization-classification scale in his 1964 paper 'Transmission of Information by Extraterrestrial Civilizations,' presented at the Byurakan Conference, based on energy use. Musk's description is essentially correct but imprecise: calling Kardashev a 'physicist' understates his identity as an astronomer, and 'Russian' is loosely accurate but more precisely 'Soviet.'