The reinsurer said in an email that it was reviewing its current business relationships in Russia and Belarus.
Swiss Re is the latest in a growing list of insurers, reinsurers, and brokers to announce plans to exit Russia.
Hannover Re, another of Europe's big four, announced last week that it had suspended new and renewal business in Russia and Belarus, while Generali, an Italian insurer, was among the first to cut ties with the country.
More recently, some of the world's largest brokers, including Marsh McLennan, WTW, and Aon, have announced plans to leave Russia in the midst of its invasion of Ukraine.
According to Reuters, a spokesperson for large insurer Zurich told the publication that the company is no longer accepting new clients and will not be renewing existing business in Russia.
The moves come as non-governmental organizations and groups around the world call on financial institutions with the most exposure to Russian oil, gas, and coal to cut all ties with these companies.
Simultaneously, rating agencies have begun to downgrade some of the country's carriers as Western nations impose tough economic sanctions on Russia, including measures designed to prevent Russian businesses from accessing international insurance and reinsurance services.