The air quality has hovered between "poor" to "severe" in the capital, which has a population of 30 million, in the last few days.
Some players and coaches from both teams trained with face masks on the eve of the match at the Arun Jaitley Stadium.
Earlier practice sessions were also cancelled while some Bangladesh players who have asthma were confined to their hotel.
The air quality index (AQI) was close to 400 near the ground, though the sunny weather has reduced the smog and improved visibility.
The World Health Organisation (WHO) advisory warns against any outdoor activities when the AQI goes over 300, which is "hazardous".
According to the International Cricket Council (ICC) guidelines air quality is usually assessed and considered by match officials and is treated as other weather matters.
Pollution in Delhi hit severe levels during a Test match in December, 2017 when Sri Lankan players came out wearing masks after the tea break.
Indian bowler Mohammed Shami vomited on the pitch.
At Sunday practice, Sri Lanka team manager Mahinda Halangoda refused to rule out similar precautions in the game.
"Obviously, today when we came, we were wearing masks, and we were told to wear masks," he said.
"But it depends exactly what the outside index is, and then we'll make a call on it."
Bangladesh coach Chandika Hathurusingha said the air quality "is not ideal".
Meanwhile, Bangladesh skipper Shakib Al Hasan won the toss and elected to bowl first in Monday's game.
Bangladesh are out of the race for the semi-finals while Sri Lanka only have a mathematical chance of making the final-four.
Bangladesh have made one change with Tanzim Hasan Sakib coming in for Mustafizur Rahman, who is "not fit enough".
Shakib said: "We have to be technically sound and also mentally sound".
Sri Lanka made two changes with Kusal Perera and Dhananjaya de Silva replacing Dimuth Karunaratne and Dushan Hemantha.
The two teams will be fighting to qualify for the 2025 Champions Trophy.
The top seven teams from this World Cup will gain entry into the tournament where hosts Pakistan will have automatic qualification.
Teams
Bangladesh: Tanzid Hasan, Liton Das, Najmul Hossain Shanto, Mushfiqur Rahim (wkt), Mahmudullah, Shakib Al Hasan (capt), Towhid Hridoy, Mehidy Hasan Miraz, Tanzim Hasan Sakib, Taskin Ahmed, Shoriful Islam
Sri Lanka: Pathum Nissanka, Kusal Perera, Kusal Mendis (capt/wkt), Sadeera Samarawickrama, Charith Asalanka, Angelo Mathews, Dhananjaya de Silva, Maheesh Theekshana, Dushmantha Chameera, Kasun Rajitha, Dilshan Madushanka
Umpires: Marais Erasmus (RSA), Richard Illingworth (ENG)
TV Umpire: Nitin Menon (IND)
Match Referee: Richie Richardson (WIS)
