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The Pakistan Cricket Board has announced Fakhar is suffering from fever and has not recovered in time for the squad's departure to New Zealand.
"Fakhar's covid test report was received on Saturday which came out negative but today he picked up fever," Pakistan team doctor Sohail Saleem said.
"As soon as his condition was reported, he was isolated from the rest of the squad in the team hotel.
We are constantly monitoring his condition and remain hopeful of his quick recovery; however he is not fit to travel with the squad and as such has been withdrawn from the touring party."
Pakistan will need a replacement at the top of their order for the three Twenty20 internationals against the Black Caps.
Fakhar averages 22.05 in T20Is, but has only once scored more than 25 runs in an innings in the last two years.
But he was the top scorer in the Pakistan's National T20 Cup and the second highest scorer in this year's PSL.
Abdullah Shafique and Haider Ali, both of whom batted in the top order at some point during the T20I series against Zimbabwe, are likely to be frontrunners to partner captain Babar Azam at the top.