Yekaterina Samutsevich, who was freed after serving several months of a two-year jail sentence over a protest against Putin in a Russian Orthodox church, likened the situation to the run-up to the 1980 Moscow Olympics, boycotted by dozens of nations.
"An event which should be purely about sport is becoming highly politicised and rife with conflict. Our authorities are to blame for that," Samutsevich told Reuters Television.
"It (a boycott) has to happen because the latest policies go too far," she said, referring to laws Putin's critics regard as repressive and criminal cases against opponents that she alleged were falsified.
"They are obviously tightening the screws," she said.
"I think a lot of people will boycott (the Games)."
Putin has staked a lot of personal political prestige on hosting a successful Games in February in Sochi, a Black Sea resort, but faces international criticism of a law banning the spread of "gay propaganda" law among minors.
Despite indignation over the law abroad, no country has said it will boycott the Olympics, on which Russia is expected to spend more than $50 billion.
At the 1980 Olympics hosted by the Soviet Union, 65 countries that were invited did not send athletes, many in protest at the 1979 Soviet invasion of Afghanistan.
Samutsevich, 31, did not specifically mention the "anti-gay" legislation but criticised a series of laws passed since Putin returned to the presidency in May 2012 that opponents say curtail rights such as free speech and assembly.
Putin denies cracking down on opponents or using the courts to persecute his critics.
Samutsevich had her sentence suspended in October 2012, two months after she and two other Pussy Riot members were convicted and sentenced for their protest in Moscow's Christ the Saviour Cathedral against Putin's close ties with the Orthodox Church.
The other two, Nadezhda Tolokonnikova and Maria Alyokhina, are due for release in early March - shortly after the February 7-23 Sochi Games.
Tolokonnikova was transferred from a prison in the Mordovia region last month after going on a hunger strike to protest conditions and an alleged death threat.
Her husband said on Thursday that after weeks of uncertainty about her whereabouts, she had been allowed a phone call and was in a hospital for convicts in the Siberian city of Krasnoyarsk, 3,300 km (2,050 miles) east of Moscow.
"It is bad that she is so far away from Moscow where she has family and her daughter Gera is," said Samutsevich, describing the move - which takes her further away from Moscow-based international media - as a "trick".
(Editing by Alison Williams)
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