Malavath, along with Sri Vidya, a 16-year-old girl from the state, began trekking the mountain on July 24 and reached the peak on July 27 at 7.30 am Moscow time, a release from the Telangana Social Welfare Residential Educational Institutions Society (TSWREIS) said.
Mt Elbrus is Europe's highest mountain peak, it said.
Malavath scaled Mount Everest, the world's tallest peak, in May 2014 when she was just 13-year-old.
Sri Vidya is from TSWREIS' school at Aleir, Nalgonda district, while Poorna is currently pursuing undergraduate course at TSWRDC (Telangana Social Welfare Residential Degree College) at Ibrahimpatnam, it said.
"As a mark of tribute, I hoisted the portrait of Chief Minister K Chandrasekhar Rao on the top of the Mt Elbrus. The chief minister sanctioned 53 welfare residential degree colleges for women and men which no other state in India has done before," the release quoted Malavath as saying.