Its usual that we see doctors use Dr. Title, but I have also seen engineers use title - Er. Is this practise allowed, approved?
I have seen few name boards like that in India.
In Europe, the approved title is Eur Ing, not Er.
It is permitted to engineers registered with one of the national engineering professional bodies.
For example, in the UK engineers must have achieved suitable qualification and registration with the IET or similar chartered organisation. Similar organisations exist in other EU countries.
Use of a prefixed title like this is much more prevalent on the continent than in the UK or US, where postfixed letters such as CEng. are much more commonly used.
Edit: The question has now been edited to refer to India. I have seen "Engineer" as a prefix on Indian business cards and office doors. That practice is not followed in Europe. Simply having an engineering degree doesn't permit such a title, you just get to put BSc. (or similar depending on the university) after your name.
In Germany it is regulated by law. So you can't just add "Dipl. Ing." if you are an engineer from outside Germany. A Dipl. Ing. is different from a Dr. since you can't have it in your passport. I've seen it as a door sign quite often.