India say they wore the caps in tribute to the country's armed forces in the wake of the killing of at least 40 paramilitaries in Indian-administered Kashmir on 14 February, in a suicide attack which has been claimed by Pakistan-based terrorist group Jaish-e-Mohammad.
The Board of Control for Cricket in India (BCCI) approached the ICC before the game about the use of the military caps, and the ICC confirmed that permission had been granted as it was part of a charity fundraising effort.
An ICC spokesperson said: "The BCCI sought permission from the ICC to wear the caps as part of a fundraising drive and in memory of soldiers who have died, which was granted."
The India players also donated their match fees for the game - which Australia won by 32 runs - to the families of those killed.
But PCB chairman Essan Mani said he has written to the ICC to protest against the caps, saying India had "tried to use cricket for politics".
Another letter was expected to be sent within hours, Mani said.
"We have made our point very strongly to the ICC which now has no doubts or confusion about our intention or stance now on this matter," he told reporters.
"Their [India] credibility in the cricketing world has gone down very badly," he added.