Australia pulled out of an upcoming series against Afghanistan in the United Arab Emirates on Thursday, citing Taliban moves to further restrict women's rights.
The men's team were due to face their Afghan counterparts in three ODI games in March following a tour to India.
"The decision to withdraw... is unfair and unexpected and will have a negative impact," the ACB said in a statement, which did not mention the shrinking of women's rights in Afghanistan nor the Taliban's ban on female sport.
The ACB said it would contact the International Cricket Council and was considering withdrawing its players from Australia's domestic Big Bash League in retaliation.
Cricket Australia (CA) said their decision was taken after talks with concerned parties that included the Australian government.
"This decision follows the recent announcement by the Taliban of further restrictions on women's and girls' education and employment opportunities and their ability to access parks and gyms," it said in a statement.
"CA is committed to supporting growing the game for women and men around the world, including in Afghanistan.
The games against Afghanistan were part of the ICC Super League.
Australia will forfeit 30 competition points for the series, which go towards World Cup qualification.
However, they have already secured automatic qualification for the 50-over tournament in India later this year.
Afghan ODI and Test captain Hashmatullah Shahidi said "fans and people of Afghanistan who have suffered immensely due to conflict... don't want politics brought into sports".
"Cricket is the most loved sport in the country and one of the main sources of happiness," he said on Twitter, asking CA to reconsider its decision.
Rashid Khan threatened to leave the BBL, where he plays for the Adelaide Strikers, in response to Cricket Australia's decision to withdraw its men's team from a bilateral ODI series against Afghanistan in March.
Rashid was recently named the captain of the Afghanistan T20I side. Rashid had replaced Mohammad Nabi, who stepped down as captain in November after Afghanistan were eliminated from the T20 World Cup.
"I am really disappointed to hear that Australia have pulled out of the series to play us in March," Rashid said. "I take great pride in representing my country, and we have made great progress on the world stage. This decision from CA sets us back in that journey. If playing vs Afghanistan is so uncomfortable for Australia, then I wouldn't want to make anyone uncomfortable with my presence in the BBL. Therefore, I will be strongly considering my future in that competition." Rashid mentioned in his tweet on Thursday.
Pace bowler Naveen-ul-Haq has already suggested he would pull out of the Big Bash League where he plays for the Sydney Sixers.
"When a country is going through so much in place (of) being supportive you want to take the only reason of happiness from them," he tweeted.
The Taliban regained control of Kabul in August 2021 and quickly began placing restrictions on women's participation in sport.
The Taliban barred teenage girls from attending secondary schools and then last month banned women from attending universities, prompting global outrage and protests in some Afghan cities.
In November, women were also banned from entering parks, funfairs, gyms and public baths.