Videos shared on social media showed supporters of both countries fighting outside the venue and security personnel being forced to intervene, while ESPNcricinfo reported that at least two fans had been evicted from the ground.
"We are aware of some scuffles among a minority of fans and are currently working with the venue security team and the local police force, West Yorkshire Police, to ensure there are no further incidents," an ICC spokesperson said.
"We do not condone this type of behaviour, and will take appropriate action against any anti-social behaviour that spoils the enjoyment for the majority of fans."
Local media reported that the trouble started when a plane towing the message 'Justice for Balochistan' flew over the venue. Balochistan is the largest province in Pakistan and borders Afghanistan to the north.
"We work with local police forces around the country to prevent this type of incident occurring and were assured that given Headingley is under the flight path for the Leeds Bradford Airport it would not be an issue," the spokesperson added.
"We do not condone any sort of political messages at the ICC Men's Cricket World Cup and will work with West Yorkshire police to deal with and understand why this has happened and to ensure it does not happen again."
West Yorkshire Police said they had been called in after "reports of some trouble outside the ground linked to people trying to get in".
"Officers attended to disperse the group without any issues and remained on patrol in the area," the police said in a statement.
(Reporting by Simon Jennings in Bengaluru; Editing by Christian Radnedge)