He will also sit out the opening Classics at Newmarket's Guineas meeting in May but he will be back in time for the Epsom Derby, which he won with Authorized in 2007, on 1 June.
Solicitor Christopher Stewart-Moore said he had spoken to father-of-five Dettori and he had no arguments with the decision by France Galop.
"He also accepts that he has let down the sport he loves and all those associated with it, as well as the wider public. But most of all - and this is his greatest regret - he has let down his wife and children," he said.
"He is enormously grateful for the opportunities that he has been given by owners and trainers over the years, and for the support of his many fans.
"Racing has been good to Frankie, and he knows that his privileged position brings with it responsibility. For this reason, he is determined to rebuild his reputation when he
returns to the saddle in six months' time."
"Frankie could make excuses - he has, after all, regularly been tested for prohibited substances throughout his career," said his solicitor.
"He is clear, however, that the responsibility for his current situation lies squarely with him. From the start of France Galop's inquiry, he has acknowledged to them that he has made a mistake and that the fault was his."
The jockey, who was given a police caution in 1993 for the possession of a small amount of cocaine in London, is not the first rider to breach the French rules.
Six-time champion jockey Kieren Fallon was banned for six months by France Galop in 2006 and then suspended for a further 18 months after a second positive drugs test in August 2007.
There are more than 400 professional jockeys in Britain. Between 2005 and 2011, a total of more than 6,000 breath and urine tests were carried out, of which seven were failed drugs tests and 13 breached the alcohol guidelines.
Cornelius LysaghtBBC horse racing correspondent
"This is nothing short of a catastrophe for the image of British racing.
"Frankie Dettori is so much more than a brilliant, world-class jockey: his bright personality, debonair looks and Italian/cockney accent have made him by far the sport's best-known character.
"Consequently, he's been considered just right to promote racing across the media, but that persona now lies in pieces.
"Back in 1993, when Dettori received a police caution for possessing cocaine, it was put down to youthful indiscretion and quickly forgotten.
"In a quite different era, as the jockey plans for life after Godolphin as a freelance, it remains to be seen just how long it takes to recover from this episode. "
The Professional Jockeys' Association (PJA) insisted the sport did not have a widespread problem with drug use, but chief executive Paul Struthers acknowledged riders did have to contend with keeping their weight down, and the possibility of falls.
"As well as all the normal pressures that other sportsmen and women have to contend with, unlike many other sports jockeys have the added pressures of massively reduced calorific intake and are constantly at very real risk of serious injury," he said.
Dettori, who passed six tests in Britain during 2012, gave the positive test at a Sunday meeting which was a day of major trials for October's Prix de l'Arc de Triomphe meeting.
The jockey had four rides at Longchamp that day.
Dettori rode Marco Botti's Joshua Tree to third in the Qatar Prix Foy, while the John Hammond-trained Sarah Lynx trailed home last in the Prix Vermeille.
He was then beaten by a head into second on the Godolphin-trained Farhh in the Prix du Moulin and was third on stablemate Willing Foe in the Prix Gladiateur.
In October, the jockey announced he was to split with Sheikh Mohammed's Godolphin operation after an 18-year association and go freelance from 2013.
Dettori has won 14 British Classics and is also a three-time winner of France's prestigious Prix de l'Arc de Triomphe, on Lammtarra in 1995, Sakhee in 2001 and Marienbard the following year.
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