But the country must re-establish a credible domestic first-class structure and its national team must play against A-sides from top-ranked nations.
Zimbabwe Cricket has also been asked to elect a board which is "inclusive".
"In-fighting has clearly contributed to disenchantment and disenfranchisement felt by players and administrators who have much to offer," The ICC said.
The Zimbabwe government took control of the cricket board in January and one of its first decisions was to withdraw the national team from the Test arena for the rest of 2006.
Several leading players, including captain Tatenda Taibu, quit the side in the months leading up to the suspension in protest at pay and the way the game was being run.
ZC chairman Peter Chingoka said a new draft constitution would be circulated on Nov 6 and a Special General Meeting would be called on Nov 18 to adopt it.
Chingoka hopes to have a new board in place on the same day.
Excluding four wins against Bangladesh, Zimbabwe have won just four other Tests since they were first admitted to the Test family in 1992.