Their Delhi camp was disrupted last month when 21 athletes and coaches tested positive for COVID-19, though they did not include any of the country's Olympic-qualified boxers.
"With a surge in COVID-19 cases, the decision was taken to shift the camp to Pune," the Boxing Federation of India (BFI) said in a statement on Wednesday.
"With the Asian Championships and the Olympic Games approaching, our focus will be to utilise the time ... and maximise the training," BFI General Secretary Hemanta Kalita said.
India reported on Thursday a record 412,262 new COVID-19 cases in the past 24 hours and a record 3,980 deaths. COVID-19 infections have now surged past 21 million in the country with an official death toll totalling 230,168.
"These are tough times but as much as we have to be careful, we also have a job at hand and we are ensuring our boxers can get back to camp and start training and working to get the best results possible," said Kalita.
Six-time world champion and 2012 London Olympic bronze medallist MC Mary Kom will spearhead India's boxing challenge in Tokyo.
Olympic-bound boxers Simranjit Kaur and Lovlina Borgohain will join her at Pune's Army Sports Institute along with seven others.
Fellow Olympic-qualified boxer Pooja Rani will continue to train in Bellary in the south Indian state of Karnataka.
India has largely struggled for Olympic success and has set itself the goal of reaching a "double digit" medal tally in Tokyo.