Rybakina is a former world No. 3 junior. She began playing on the ITF Junior Circuit in November 2013 at the age of 14. The following March, she won her first title at her second career event, the Grade-3 Almetievsk Cup. She played her first Grade-2 event in June at the Ozerov Cup in Moscow, finishing runner-up to compatriot Anna Blinkova. She began playing Grade-1 events from the start of 2015, but did not have any success until she reached the final at the Belgian International Junior Championships in May, losing to Katharina Hobgarski.

Rybakina made her junior-Grand Slam debut later in the year at the US Open, where she reached the third round. Following an opening-round loss at the 2016 Australian Open, she won back-to-back Grade-1 titles. She continued to struggle at the junior Grand Slam and other Grade-A events in singles for the rest of the year. Her best result of 2016 at the Grade A-events came in doubles when she finished runner-up to Olesya Pervushina and Anastasia Potapova at the Trofeo Bonfiglio, alongside Amina Anshba in an all-Russian final.

The 2017 season was Rybakina's last year on the junior tour. In the middle of the season, she won her first and only Grade-A title at the Trofeo Bonfiglio, defeating Iga Świątek in the final. She also fared better at the Grand Slam events compared to previous years, losing in the semifinals of the Australian Open and the French Open to eventual champions Marta Kostyuk and Whitney Osuigwe, respectively. She finished her junior career at the first round-robin edition of the ITF Junior Masters, the junior counterpart to the WTA Finals. She won one match in her round-robin group and finished in seventh place.