"Anas Haqqani visited the cricket board and told me very clearly that my job as the (chief) executive officer was over," Shinwari wrote on his Facebook page.
Anas Haqqani is a senior Taliban official and the younger brother of Afghanistan's new interior minister Sirajuddin Haqqani.
Shinwari's post, seen by AFP, was later not visible, with the page apparently deactivated. In the Pashto language post, Shinwari said he had asked for a formal order but did not receive it.
"I was elected to the Cricket Board's executive section after a transparent process, but I did not understand the reason for my dismissal," Shinwari said.
He was later replaced by Naseebullah Haqqani, also known as Naseeb Khan, a close ally of the Haqqani network, said a source at the cricket board who did not want to be named.
"He holds a master's degree and has knowledge of cricket as well," the board said on its Facebook page.
During their first stint in power, before they were ousted in 2001, the Taliban banned most forms of entertainment -- including many sports -- and stadiums were used as public execution venues.
But the hardline Islamists do not mind cricket and the game is popular among their fighters. Women were completely banned from the game under the last regime, and no directive has yet been released on female participation this time around.