The MBA (Master of Business Administration) is a postgraduate degree that is awarded to students who have mastered the study of business. The MBA degree is thought to be one of the most prestigious and sought after degrees in the world.
No there is no Institute in India that require Two Years Work Experience

Here I am providing you name list of the Top MBA institutes of India:
Indian Institute of Management, Bangaluru
Bannerghatta Main Rd, Bilekahalli, Bengaluru, Karnataka 560076
080 2658 2450

Indian Institute of Management, Ahmedabad
Indian Institute of Management , Vastrapur, Ahmedabad 380015
9.478996655

Indian Institute of Management, Calcutta
Diamond Harbour Road, Joka, Kolkata, West Bengal 700104
033 2467 8300

Indian Institute of Management, Lucknow
Prabandh Nagar, IIM Road, Lucknow, Uttar Pradesh 226013
0522 273 4101

Indian Institute of Management, Udaipur
Polymer Science Building, Mohanlal Sukhadia University Campus, University Road, Ganesh Nagar, Udaipur, Rajasthan 313001
0294 247 7106

Indian Institute of Management, Kozhikode
Konnamangalam, Kozhikode, Kerala 673570
0495 280 9100

International Management Institute, New Delhi
B-10, Qutab Institutional Area, Tara Crescent, New Delhi, Delhi 110016
011 4719 4100

Indian Institute of Forest Management, Bhopal
Nehru Nagar, Shastri Nagar, Bhopal, Madhya Pradesh 462003
0755 277 5716

Indian Institute of Technology, Kanpur
Kalyanpur, Kanpur, Uttar Pradesh 208016
0512 259 0151

Indian Institute of Management, Indore
Prabandh Shikhar, Rau Pithampur Road, Indore, Madhya Pradesh 453556
0731 243 9666