"We watched what happened in Zimababwe," said ICC chief executive Malcolm Speed, who is in Pakistan to watch the ongoing third and final Test with England.
"There is a daily report on the Zimbabwe issue, but the ICC policy, which is made by its member countries and applicable to all, leave the internal matters to the respective country.
"At the ICC we think basically all internal matters should be dealt by the country concerned."
Taibu quit last week citing "the deteriorating state of the Zimbabwe cricket administration and failure to obtain a satisfactory contract after months of negotiations". His decision was also prompted by threats of violence.
A group of Zimbabwe national team cricketers are scheduled to meet this week after making up their minds whether to stay with the team or seek new careers.
"I am saddened by the Zimbabwe issue. The resignation of their captain is a significant blow to cricket in Zimbabwe," England and Wales Cricket Board (ECB) chairman David Morgan said after the second day's play here.
Zimbabwe have lost many top players in recent years.
Most notably, wicketkeeper-batsman Andy Flower and the first black player Henry Olonga had to leave the country after their black armband protest over their "death of democracy" in the country during the 2003 World Cup.