Both firms, along with the other main rating agency, S&P Global, have also withdrawn or suspended ratings on a number of the most heavily-sanctioned Russian and Belarussian banks, including VTB , Promsvyazbank (PSB) and Sovcombank.
"Fitch Group has decided to suspend its commercial operations in Russia with immediate effect," Fitch said in a statement, saying that involved credit ratings and some other services it provides.
It added it would comply with "all applicable sanctions", support its Russia-based staff and "continue to provide the market with its independent analytical views through ratings coverage undertaken outside of Russia."
Russia's financial markets have been in a turmoil due to the sanctions imposed over its invasion of Ukraine, the biggest attack on a European state since World War Two.