Medvedeva's international debut came in the 2013–2014 season. Competing on the ISU Junior Grand Prix series, she won gold first in Riga, Latvia, and then in Gdańsk, Poland. She qualified to the JGP Final in Fukuoka, Japan, where she won the bronze medal behind Sotskova and Serafima Sakhanovich. At the 2014 Russian Championships, she finished seventh in her second senior appearance and then fourth on the junior level. Medvedeva was assigned to replace the injured Sotskova at the 2014 World Junior Championships in Sofia, Bulgaria. Placing third in both segments, she won the bronze medal while Elena Radionova and Sakhanovich took gold and silver respectively, producing Russia's second consecutive sweep of the World Junior ladies' podium.