Yes, ISI Kolkata MTech CS coursework include an internship. You need to do an internship in industry or in academia, during the summer after your first year. There are three types of internships.

Industry Internship - Companies recruiting through ISI Kolkata placements, also select interns. MTech CS students have done internships from Google, Samsung Research Lab, JP Morgan Chase, Reliance, etc. Students receive an average stipend of around INR 65,000/month.

Internships from Universities - ISI also gives the option to do internships from other institutes. Many do their internships at universities abroad. Students also go to tier 1 Indian institutes such as IIT, CMI, etc. 

Internship at ISI -  Students also have the option to do internships at ISI. 

After first year, you will have summer internship and in second year you will have placements and dissertation. If you want to do an additional internship, the only time will be winter after the first sem.