Essex, who appointed Akhtar on Monday, said in a statement they supported the decision and named Stephen O'Brien as interim chair.
"We remain committed to tackling discrimination and racism and have a zero-tolerance approach in this area," Essex said.
"All of those connected with Essex want to ensure the Club is a safe and welcoming place where everyone, no matter of background, can play a major part in the future of Essex Cricket."
Akhtar said in a separate statement he wanted to show leadership by stepping aside to "ensure the club can focus on the ongoing challenges it is tackling".
Previous Essex chairman John Faragher resigned in November last year over a historical allegation, which he strongly denied, that he used racist language at a board meeting in 2017.
Essex were fined 50,000 pounds ($61,000) by an independent Cricket Discipline Commission panel in May after pleading guilty to two charges in relation to that meeting.
The England & Wales Cricket Board (ECB) also reprimanded and cautioned the club about further conduct, with 15,000 pounds of the fine suspended for two years.
