The Russian tennis player (sixth seed) in the first round match outplayed Angelina Kalinina from Ukraine in three sets with a score of 5:7, 6:3, 6:1.
The next opponent of 25-year-old Kasatkina will be the winner of the meeting between compatriot Ekaterina Alexandrova and Marina Zanevskaya from Belgium.
The total prize fund of the tournament in Berlin is more than $750,000.
Earlier, State Duma deputy Svetlana Zhurova spoke about the return of Medvedev to the first line of the ATP rating.