APEX 5.0 comes with a new calendar region, which is way nicer than the previous calendar in APEX. It has more features, looks better and is also responsive. Behind the scenes you'll see the calendar region is based on Full Calendar.
In APEX 5.0 I looked for that option, but there's not a specific attribute to set the first day of the week, instead it's based on the language of your application. If you go to Shared Components > Globalization Attributes by default it's set to en, which has Sunday as start of the week. If you set it to en-gb it will have Monday as start of the week.
I searched some time to find how to do it, so hopefully this post will help others to find it more easily. Thanks to Patrick for sharing the way it was implemented.