Yes there are few NIT's that provide mechatronics program:

NIT Rourkela

NIT Hamirpur

There are few IIT's which also offer this program like
IIT Kanpur,

IIT Delhi,

IIT Bombay

IIT Patna

IIT Madras

Also University of Petroleum and Energy Studies(UPES) does have a Mechatronics dept.

Hope this helps!

Thank you

Here are the top 10 mechatronics engineering colleges in india given below-

1. NATIONAL INSTITUTE OF TECHNOLOGY - [NITK] KARNATAKA, SURATHKAL
2. INDIAN INSTITUTE OF TECHNOLOGY - [IIT], PATNA
3. SRM UNIVERSITY AMARAVATI, GUNTUR
4. VELLORE INSTITUTE OF TECHNOLOGY - [VIT UNIVERSITY], VELLORE
5. LOVELY PROFESSIONAL UNIVERSITY - [LPU], JALANDHAR
6. NATIONAL INSTITUTE OF TECHNOLOGY - [NIT], ROURKELA
7. INDIAN INSTITUTE OF ENGINEERING SCIENCE AND TECHNOLOGY - [IIEST] SHIBPUR, HOWRAH
8. NARSEE MONJEE INSTITUTE OF MANAGEMENT STUDIES - [NMIMS DEEMED TO BE UNIVERSITY], MUMBAI
9. MANIPAL INSTITUTE OF TECHNOLOGY - [MIT], MANIPAL
10. SRM ENGINEERING COLLEGE, KANCHIPURAM