After studying under Felice Ronconi and Francesco Lamperti, Dodonov sang with the Italian Opera in Milan and Naples, then in Odessa and Kiev. From 1869 to 1891 Dodonov he was a soloist at the Bolshoi Theatre in Moscow, where he premiered a number of roles in Tchaikovsky's stage works: Frost (in The Snow Maiden), the Drunken Cossack in Mazepa (1884), the School Teacher in Cherevichki (1887), and the tenor solo in the Cantata for the Opening of the Polytechnic Exhibition (1872).
Dodonov published his Handbook to the Correct Interpretation of Voice and Leaning the Art of Singing (Руководство к правильной постановке голоса и изучению искусства пения) in 1891, and later became a professor at the Moscow Philharmonic College of Music and Drama.
In 1875 Tchaikovsky dedicated one of his romances to Aleksandr Dodonov:
- The Corals — No. 2 of the Six Romances, Op. 28.