Kaliningrad, with a population of around 430,000 people, is wedged between Lithuania and Poland, both EU countries, and is isolated from the rest of Russia.
Nikolai Patrushev, the powerful secretary of the Kremlin's Security Council and a hardliner, visited Kaliningrad on Tuesday and vowed to respond to the ban.
"The relevant measures are being drawn up in an interagency format and will be adopted shortly," Patrushev said, without elaborating. He added: "Their consequences will have a significant negative impact on the population of Lithuania."
Meanwhile, Russian authorities blocked the website of British newspaper The Telegraph over an article it published, the internet rights group Roskomsvoboda reported Tuesday.