A Pakistan Cricket Board official told BBC Sport one drone misfired and led to an explosion in the street behind the stadium in Rawalpindi. The BBC has been unable to verify these claims.
The PSL had been looking at all options for the remainder of the campaign, including halting the tournament for a number of weeks.
The exact schedule for the rest of the tournament, including dates and venues in the UAE, has yet to be confirmed.
Players at the PSL, including those from England, took part in an emergency meeting held by tournament organisers on Thursday.
James Vince, Chris Jordan, Tom Curran, David Willey, Sam Billings, Luke Wood and Tom Kohler-Cadmore are the English players involved in the PSL, while there are also English coaches at various franchises.
PSL organisers remain keen for the tournament, which has eight fixtures outstanding, to be completed, but the safety of players remains their priority.
A senior Pakistan Cricket Board (PCB) official told BBC Sport: “If Rawalpindi is not safe, Lahore and Karachi are not safe because drones also attacked there. Any city of Pakistan is not safe because the drones have targeted smaller cities of Pakistan.”
The seven English players held separate discussions over whether to return to the UK, with a split in opinion over whether to remain.
Talks took place with the Professional Cricketers’ Association (PCA) on Wednesday to discuss the situation. It is understood feelings among those in Pakistan were mixed.
Other leading overseas names in the PSL include Australian David Warner (Karachi Kings) and former West Indies captain Jason Holder (Islamabad United).
The UK foreign office currently advises against all but essential travel within five miles of the international border between Pakistan and India.
The Indian Premier League match between Punjab Kings and Delhi Capitals began as planned in Dharamsala on Thursday, but was called off after 10.1 overs after the floodlights went out.
Sunday’s match between the Kings and Mumbai Indians has been moved from Dharamsala to Ahmedabad.
Dharamsala is in the state of Himachal Pradesh, which borders Kashmir, and flights were cancelled to its airport on Wednesday, making it difficult for Mumbai Indians to travel.
“The venue change has been necessitated due to logistical challenges,” India’s cricket board (BCCI) said in a statement.
Twenty-six civilians were killed in Indian-administered Kashmir last month and India has accused Pakistan of supporting militants behind the attack – an allegation the neighbouring country has rejected.
The situation escalated on Tuesday evening when India launched a series of strikes in a move named “Operation Sindoor”.
