The bowler was grounded at Heathrow due to the weather conditions while looking to meet up with the England side for their final two one-day internationals.
Coach Ashley Giles told the ECB's website: "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.
"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."
Broad has not played since November due to a heel injury.
England are due to play a Twenty20 against New Zealand in Auckland on February 9.