Data scientist Amrit Sharma, who made the request in an open letter to Mr Obama, said doing so would help generate awareness and catalyse action on air pollution.
Delhi's air quality remained in the "very poor" category for the seventh straight day on Thursday with the Central Pollution Control Board (CPCB) recording an AQI (air quality index) of 360.
Mr Sharma has also been invited to attend the interactive session with Mr Obama at the town hall.
"You are one the most photographed people on earth, but none of your photos could potentially save millions of lives yet. I believe that if you wear a face mask while you are in Delhi and take a photo (of it), that alone could have such an impact," Mr Sharma wrote in the open letter to Obama.
He acknowledged that in a developing country like India, a vast section of the population could not afford the expensive face masks, let alone an air purifier.
However, he said, Mr Obama wearing a mask at a public forum might spur the authorities into action.
Delhi's air quality was under an intense scanner when Barack Obama had attended the 2015 Republic Day parade as the chief guest.