Pussy Riot member Maria Alyokhina has left Russia, she said in an interview, after disguising herself as a food delivery courier to escape police. 

Alyokhina joins thousands of Russians that have fled their country since President Vladimir Putin sent troops into Ukraine on February 24. 

In September, Alyokhina was sentenced to one year restricted movement while protesting in support of jailed Kremlin critic Alexei Navalny, but in April authorities moved to convert her sentence into real jail time. 

In an interview with the New York Times late on Tuesday, Alyokhina, 33, described how she dressed up as a food courier to avoid the Moscow police that were staking her out and left her cellphone behind so she couldn't be tracked.

Then a friend drove her to the border with neighbouring Belarus and a week later she managed to cross into EU member Lithuania after several attempts, according to the interview. 

"I was happy that I made it, because it was an unpredictable and big 'kiss-off' to the Russian authorities," she told NYT.

Her partner and fellow Pussy Riot member Lusya Shtein posted a photo of Alyokhina on Twitter, dressed in a green Delivery Club uniform and wearing a food delivery backpack. 

Shtein tweeted that Alyokhina "did not flee Russia, she has gone on tour" to raise money for Ukraine that will start with a concert in Berlin on May 12.

Shtein was also sentenced to restricted movement over Navalny protests but in April she fled Russia, posting a video of herself cutting off a police anklet monitor. 

A veteran member of the Pussy Riot feminist group, Alyokhina spent two years in prison for taking part in the group's 2012 protest performance in neon balaclavas inside Moscow's Christ the Saviour Cathedral.