I am thinking of pursuing MBA in Data Science in Europe.

What degrees are available? What European country is best to study Data Science?

The MBA isn't a specialised degree in Europe in the way it is, for example, in India. A European MBA is a degree in general management, while a master's in data science would typically be a MSc, rather than an MBA. An MBA in data science would, in Europe, be a weird degree aimed at students returning to Asia.

Yes. There are specialized MSc programs in Data Science (EDHEC has a decent one), which are typically aimed at early career professionals who want to specialize in this area.

MBAs are usually aimed at more senior professionals (3-7 years of work experience) and most European MBAs would not be 'specialized' in this way. Some allow you to choose concentrations or specializations, though.