The former Dire Straits frontman is scrapping the June gigs in Moscow and St. Petersburg following raids on the Russian offices of groups including Human Rights Watch and Amnesty International, according to a post on his website Friday.
"I have always loved playing in Russia and have great affection for the country and the people," he said in the post. "I hope the current climate will change soon."
Russian authorities raided hundreds of non-governmental organizations last month to make sure they comply with a law requiring many of them to register as "foreign agents."
The government says the law is designed to curb foreign meddling, but critics say it is intended to stifle dissent.
Putin said Friday the non-governmental organizations must account for their foreign funds.
Speaking in an interview with the German ARD television that was released by the Kremlin, Putin said the government wants to know "who is getting the money and how they are spent." The searches of around 2,000 NGOs, seen as part of Kremlin crackdown on dissent, have drawn strong protests from international rights groups and Western governments.
Putin has repeatedly accused NGOs of being a tool for Western interference in Russia's affairs. Speaking to ARD before his trip to Germany, he said the checks are to make sure the NGOs comply with a new law requiring those who get foreign funds to register as "foreign agents."