Kalinina twisted her leg at the beginning of the second set and could not immediately get up from the court on her own.
The Russian tennis player ran up to her opponent with an ice pack.
Kasatkina (sixth seed) in the first round match outplayed Kalinina in three sets with a score of 5:7, 6:3, 6:1.
The next rival of 25-year-old Kasatkina will be the winner of the meeting between her 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.