If the day/month components could be one or two digit characters, then you should use this pattern:
^\d{1,2}\.\d{1,2}\.\d{4}-\d{1,2}\.\d{1,2}\.\d{4}$
Demo
Presumably the years might also not be fixed width, but it is probably unlikely that a year earlier than 1000 would appear, so we can fix the year at 4 digits. Also, literal dot in a regex pattern needs to be escaped with a backslash.
Edit:
If you want to first validate the string, and then separate the two dates, then consider this:
String input = "3.06.2019-20.06.2019";
if (input.matches("\\d{1,2}\\.\\d{1,2}\\.\\d{4}-\\d{1,2}\\.\\d{1,2}\\.\\d{4}")) {
String[] dates = input.split("-");
System.out.println("date1: " + dates[0]);
System.out.println("date2: " + dates[1]);
}