Selling concert tickets "is highly contradictory to the principles of Pussy Riot," said the letter, which was signed with six nicknames.
"We're a female separatist collective," it said. "We never accept money for our performances," and "we only stage illegal performances in unexpected public places."
The letter also took issue with posters for the concert that showed a male guitarist in a balaclava, a trademark of the feminist group.
Neilson Barnard, Getty/AFP
Maria Alyokhina (L) and Nadezhda Tolokonnikova of Pussy Riot speak onstage at the Amnesty International Concert presented by the CBGB Festival at Barclays Center on February 5, 2014 in New York City
Tolokonnikova, 24, and Alyokhina, 25, were freed from Russian penal colonies in December three months before the end of their two-year sentences for staging an anti-Putin "punk prayer" performance in a Moscow cathedral.
They said on their release that they would focus on campaigning for the rights of prisoners.
Wednesday's concert in Brooklyn saw performances by The Flaming Lips and Blondie. Ticket prices started at $27.
"They have said in every interview that they have quit the group and no longer represent Pussy Riot," said the letter. "But all of their appearances are announced as appearances by Pussy Riot."
"They are no longer Pussy Riot," said the appeal signed by nicknames Cat, Garadzha, Fara, Shayba, Serafima and Shumakher.
"We have lost two friends, two ideological teammates, but the world has gained two brave rights activists," they said.
Five members in colourful tights and balaclavas staged the fateful cathedral performance in February 2012, with three arrested the following month.
One, Yekaterina Samutsevich, was later freed with a suspended sentence after a successful appeal.
The other two performers have never been identified.
Since the women were arrested, there have been no more guerrilla Pussy Riot performances in public places, although a music video targeting Russia's oil industry was published in July 2013, apparently by a splinter group that had set up a new website.