The Pakistan Cricket Board (PCB) had written to the governing body complaining about a visa delay which, it said, had disrupted the team's preparation for the showpiece event across the border.
"Visas have been issued to the Pakistan team," an ICC spokesperson told Reuters without elaborating further.
PCB spokesperson Umar Farooq confirmed to Reuters they have been asked to collect their passports from the Indian high commission in Islamabad.
India and Pakistan have suspended bilateral cricket, thanks to a soured political relations between the neighbours, and play each other only in multi-team events like the World Cup and Asia Cup.
Earlier in a strongly-worded statement, Farooq decried the "inequitable treatment" metered out to a Pakistan team, who are scheduled to arrive in India on Wednesday.
"There has been an extraordinary delay in getting clearance and securing Indian visas for the Pakistan team for ICC World Cup," Farooq said in the statement.
"We have written to ICC raising our concerns about inequitable treatment towards Pakistan and reminding them of these obligations towards the World Cup.
"It's a matter of disappointment that the Pakistan team has to go through the uncertainty ahead of the major tournament."
Pakistan will play two warm-up matches before beginning their World Cup campaign against the Netherlands on October 6th.
Arch-rivals India and Pakistan are set to clash in a mouth-watering October 14th contest in Ahmedabad.
India declined to tour Pakistan for the Asia Cup, which was played between August 30th and September 17th, and played their matches in Sri Lanka instead.