The incident occurred when some of the people leaned on a wall causing its collapse.
A man and woman were injured in the mishap. They were immediately rushed to a nearby hospital.
They were discharged from the hospital after the treatment as they had sustained minor injuries.
Four cricket matches for the world cup will be held in the stadium.
This is the second embarrassment for India in connection with the World Cup.
TNCA officials described the incident as “minor” and said ticket sales were not disrupted due to the mishap.
They said about 50 people of the nearly 3,000-odd strong crowd suddenly pushed towards the wall, resulting in a portion of it caving in.
Earlier, Kolkata’s Eden Garden was declared unfit to host a match between India and England. The match has been shifted to Bangalore.