"Do you plan a serious, sincere, honest liberalisation, a real democratisation of the country so that NGOs stop being strangled and people stop being afraid of policemen on the street?" he asked.
Shevchuk, who is known for his outspoken opposition views, questioned Putin at a charity event in Saint Petersburg.
Their encounter was shown edited on state television, but a transcript was published on the Kremlin website Saturday evening.
Putin reacted sharply to questioning, asking Shevchuk "Is that all?" and several times angered him for interrupting.
He also claimed not to know the name of the shaggy-haired rocker, who leads one of Russia's most popular and long-lived bands, DDT.
Shevchuk's grilling prompted the prime minister to give unexpected support for an opposition rally planned for Monday.
The authorities should not "create impossible conditions for the expression of freedom of speech," Putin said.
Opposition supporters including Shevchuk plan to hold a Dissenters' March rally on Saint Petersburg's Palace Square on Monday evening.
Police have regularly detained opposition activists including former world chess champion Garry Kasparov at the rallies held around Russia over the last four years.
Shevchuk praised Putin for a "normal, serious, man-to-man conversation" in comments to Fontanka.ru news website.
The prime minister "was not afraid of an open conversation and behaved like a normal person," he told the website after the meeting.
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