Yes, you will get opportunities at IIT Madras to pursue internships in foreign universities provided that you have your faculty advisor’s permission since you are working under his guidance.
If he is a reasonable man, there is no justified reason to stop you from going for internships. Try to make your point clear and tell them you are willing to get more exposure. Your guide is a knowledgeable person and won’t deny your request if you approach him with a reasonable stance.
However, in case he suspects your work to suffer because of the internship, he may stop you. If you haven’t met the work standards he has set or have dissatisfied him in some other way, be ready to get reprimanded. But this is a very rare scenario as an internship offer is as beneficial to him as it is to you.