Russia was banned from competing by the International Paralympic Committee (IPC) following allegations of state-sponsored doping.
After a failed appeal at the Court of Arbitation for Sport (Cas), an appeal to the Swiss Supreme Court had been Russia's last hope of being in Brazil.
However, it will now miss the Games, which begin on 7 September.
More than 100 Russian athletes wrote to the IPC asking it to overturn the ban.
However, the Swiss Supreme Court said the Russian Paralympic Committee had not shown it had "fulfilled its obligations to anti-doping rules".
Russia has failed in its final attempt to reverse the ban on its athletes from next month's Rio Paralympics.