The silver and the bronze medal went to two German athletes: Nadine Muller (63.00) and Shanice Craft (62.46).
Perkovic, born on 21 June 1990 in Zagreb, is a two-time Olympic (2012, 2016) and World (2013, 2017) champion.
The European Athletics Championships in Berlin is being staged 7-12 August and Perkovic's medal is the first for Croatia.
She is the first athlete to win five European titles in a row in the track and field contests.