Hi, Yes Anna University provides technology management course in distance mode. The eligibility states:

1. A pass in any Bachelor Degree* and
2. A pass in Distance Education Entrance Test (DEET) conducted by the CDE, Anna University, Chennai.

3. The Bachelor Degree must have been obtained after +2 or equivalent.

This branch of management is available in India and abroad. This program excels one  in technological field.

Technology management is a potential MBA specialization often offered within some MBA and Executive MBA programs. In many cases, those enrolled in an Executive MBA in Technology Management program are likely working professionals who've been in their field for ten or more years.

One will study about managerial economics, such as supply and demand, production technology, costs and operation of markets; concurrently, will learn about the use of technological tools and systems to address these areas. You shall get to study IT aspect as well. You will also design and implement database management systems. 

Because you have an engineering background you can even go for Mtech.

Talking about distance/regular MBA then the prospects of a full time regular management course are better than a correspondence or distance learning course. Practically the acceptability and recognition of a full time course is higher in industry whereas distance learning courses are ideally meant for some purspose or the need of the student. Those who follow the distance route need to try some what harder to get good jobs, but if you have the required talent, calibre and knowledge and above of all could justify your reason to study from distance mode then you can definitely choose this mode of education.

Hope this helps to you the maximum extent.

Good Luck.