This theatre "is one of the most popular theatres in Russia, and its excellent collection of puppets includes all known puppetry techniques from classical times to the present day," Gelena Iliyina, Russia's cultural attache in Croatia, said at the opening ceremony.
The collection boasts about 4,000 puppets, which makes it one of the largest in the world.
The Zagreb show features about 40 puppets that were designed in Russia, some of which were used in the play Princess and the Pea that preceded the opening ceremony.
The exhibition closes on September 5.