New Delhi topped a real-time list of the world's most polluted cities compiled by Swiss group IQAir, which put the city's air quality index (AQI) at 640 in the "hazardous" category on Friday.
Bangladesh cancelled their training on Friday because of the toxic haze, which has blanketed the city where some schools were ordered closed as the AQI plummeted.
The organising Indian cricket board (BCCI) has already banned use of fireworks in post-match celebration in New Delhi and Mumbai.
The governing International Cricket Council (ICC) said it was monitoring the situation in New Delhi.
"We are currently assessing the situation," an ICC spokesperson said in a statement to Reuters.
"The ICC and our hosts the BCCI take the wellbeing of all participants seriously and are monitoring the air quality in Delhi.
"We are taking expert advice to assess the situation."
During an India v Sri Lanka test match in New Delhi six years ago, several players vomited on the field, while others struggled with the hazardous air.
Air quality has been abysmal in Mumbai as well and England player Joe Root (32) said it felt like they were "eating the air" in the western Indian city.
India captain Rohit Sharma (35) has also spoken about the worsening air quality.
"It is not ideal and everyone knows that," Rohit said on Wednesday worried about its impact especially on children.
"Obviously it is important that they get to live without any fear," Rohit said.
"Every time I get to speak outside of cricket, or not discussing cricket, I always talk about this. We have to look after our future generations."