The International Association of Athletics Federations informed Klishina last week that it has withdrawn her name from the Olympics and other competitions based on new information it received, said IAAF spokesman Yannis Nikolaou.
The IAAF was not able to comment on what new information this was.
Klishina, a world youth champion in 2007, is challenging the decision with CAS.
"I am a clean athlete and have proved that already many times and beyond any doubt," she said on Facebook. "(Having been) based in the US for three years now, I have been almost exclusively tested outside of the anti-doping system in question.
"I am falling victim to those who created a system of manipulating our beautiful sport and (are) guilty of using it for political purposes."
A decision on the case is expected within in a couple of days, Nikolaou said. The women's long jump is scheduled to begin Tuesday.
The secretary-general for the Court of Arbitration for Sport, Matthieu Reeb, confirmed the appeal to CNN via email but had no further details.
With Klishina's suspension, Russia no longer has any athletes competing in track and field in Rio. The IAAF ruled out the other 67 athletes on the Russian athletics team before the Games began.
Also Saturday, the The World Anti-Doping Agency announced that someone illegally accessed the WADA database account of Yuliya Stepanova, one of the key whistleblowers in exposing state-run doping in Russia.
No other athlete accounts were compromised, WADA said. Thousands of athletes have accounts on the system, which is used to log their anti-doping information.