Some Russian lenders have started charging fees for accounts in dollars and euros as the sanctions-hit sector grapples with its new reality since Moscow sent troops into Ukraine in February.
Tinkoff has introduced a commission on incoming SWIFT transfers.
The lender has not been directly targeted with sanctions, but major Russian banks have been cut off from SWIFT, the messaging system underpinning global financial transactions, transfers which Tinkoff said were 95% dependent on Western payment infrastructure.
"We are forced to admit that our efforts to ensure that our Western partners fulfilled their part of the arrangements within a reasonable and comfortable time frame for our clients have not been enough," Tinkoff said on its Telegram channel.
Tinkoff said it would donate all the money it has received from commissions and fees on foreign currency accounts and transfers to charity.
"We will make every effort to ensure that all SWIFT transfers from customers awaiting processing are fulfilled within a reasonable time frame," Tinkoff said.
"The average time frame for carrying out SWIFT transfers of Russian customers is already reaching several weeks and will continue to increase."
TCS Group ringfenced its Russian business in early April, transferring shareholder's authority over Tinkoff Bank to its Russian management team.
In a separate statement on Wednesday, Tinkoff said it had successfully facilitated a rouble cross-border payment from a Russian bank to one in Kyrgyzstan, using the Bank of Russia's Faster Payments System (FPS), a widely-used service in Russia that enables phone-to-phone instant transfers.
Tinkoff said it planned to give Russian banks access to cross-border transactions for some countries in the future.
"Transfers from foreign banks to Russia are planned to launch by the end of 2022."
(Reporting by Reuters; editing by Jason Neely)