He was 80 and is survived by his wife, two sons and a daughter.
Polly Umrigar had been undergoing chemotherapy after being detected with cancer for the last few months. His funeral will take place on Wednesday morning, according to family sources.
Umrigar had played in 59 Test matches for India in a career spanning from the 1940s to the 1960s, scoring 3631 runs, an Indian record at that time, at an average of 42.
Colonel schoked: Former India captain Dilip Vengsarkar today expressed shock at the passing away of India's all time great cricketer and former captain, Polly Umrigar.
Reacting to the news of the passing away of Umrigar, Vengsarkar, nick-named as colonel by Polly kaka, expressed total shock at hearing the news.
After regaining his composure he said he had learned a lot from Polly Umrigar. ''Umrigar had been our manager on a couple of occasions and he was not just a great cricketer from whom you could learn a lot about cricket, but also a great and warm human being,'' Vengsarkar said.
This is a void which would be impossible to fill, Vengsarkar added.