With the weather conditions not likely to improve quickly, Broad would have struggled to reach India in sufficient time before the fourth ODI to be played at Mohali on January 23.
"Gutted I can't get to India. I'm off home with all my luggage at Heathrow. I'll be waiting for the lads in New Zealand!!" Broad tweeted.
It was not certain whether he would have played in the last two matches but at least he would have trained with the team in India.
He will now join the team in New Zealand for the first warm-up match on February 4, ahead of the Twenty20 series for which Broad will resume the captaincy. He had also missed England's two Twenty20 International matches against India before Christmas due to injury.
England limited-over coach Ashley Giles confirmed that Broad will not join the squad after his flight from England was cancelled.
"Stuart is not coming to India now. He got snowed in at Heathrow and I think his bags went missing as well, so he is going to join us out in New Zealand," Giles was quoted as saying by 'Daily Mail'.
"It's not ideal because we were hoping for him to come out here and, whether or not he played in one of the last two games, just do some prep for New Zealand. But we have a bit of time in New Zealand and he'll meet us there. It can't be helped; you can't do much about snow."