Eleven horses based at Newmarket in southern England tested positive for steroids, including stanozolol - the substance used by disgraced Olympic sprinter Ben Johnson at the 1988 Seoul Olympics.
Announcing the date for the disciplinary hearing, the BHA said Al Zarooni had also admitted administering prohibited substances to four other horses under his care, in addition to the 11 that were tested positive.
On Tuesday Al Zarooni, who works for Dubai ruler Sheikh Mohammed bin Rashid Al Maktoum's stable, said he regretted what he described as "a catastrophic error".
Sheikh Mohammed said in a statement: "I was appalled and angered to learn that one of our stables in Newmarket has violated Godolphin's ethical standards and the rules of British racing.
"I have been involved in British horse racing for 30 years and have deep respect for its traditions and rules. I built my country based on the same solid principles. There can be no excuse for any deliberate violation.
"Godolphin is fully cooperating with the British Horseracing Authority to get to the bottom of this matter and take any appropriate disciplinary action.
"I have ordered the Godolphin management to undertake an immediate review of our internal procedures and controls to ensure to prevent any reoccurrence of this type of activity in any stables of mine.
"We will be locking down the Moulton Paddocks stables with immediate effect, and I have instructed that I want a full round of blood samples, and dope testing done on every single horse on that premises.
"I can assure the racing public that no horse will run from that yard this season until I have been absolutely assured by my team that the entire yard is completely clean.
"I have worked hard to ensure that Godolphin deserves its reputation for integrity and sportsmanship, and I have reiterated to all Godolphin employees that I will not tolerate this type of behaviour."
Samples were taken from 45 horses at Godolphin's Moulton Paddocks Stables on April 9.
Eleven samples were found to contain prohibited substances including ethylestranol and stanozolol.
One of the horses to test positive was Certify. The filly will not now be allowed to take part in the 1,000 Guineas at Newmarket next month.
Unbeaten in four career outings, Certify was one of seven horses to test positive for ethylestranol. Gold Cup runner-up Opinion Poll was one of four to test positive for stanozolol.
Founded in 1992, the Godolphin stable has won more than 2,000 races worldwide with winners in 14 countries.