According to a statement posted on the two Michelin-starred restaurant's website, 63 out of 435 diners fell ill in the second week of February (February 12 - 16).
The outbreak of the so-called winter vomiting virus was reportedly due to a staff member who was a carrier for the bug but was not showing any symptoms.
"At Noma, having happy and satisfied guests is paramount to our daily work and lives, and is our number one priority," said Redzepi in the statement.
"Unfortunately during week seven, there were a number of cases were guests at Noma where hit by norovirus after their visit. It is a matter that deeply affects us all, and that we sincerely regret," he said.
An inspection of the restaurant was conducted by Fødevarestyrelsen, the Danish Veterinary and Food Administration run by the Ministry of Food, Agriculture and Fisheries, on February 20.
The inspection was made after one of the diners affected emailed both the restaurant and Fødevarestyrelsen.
Noma was given the all-clear by the authorities after putting in new guidelines after the outbreak. The results of the inspection were posted on the front door to the restaurant and the venue's website.
However, a Danish news website published the results on Friday which resulted in widespread worldwide attention and frenzied, often incorrect, reporting from a number of media organisations.
One report claimed Noma had been criticised for not providing hot water for staff to wash their hands - in reality one of four sinks had lukewarm, as opposed to hot, water, a situation resolved immediately.
In the face of the furore surrounding the story, Redzepi released a lengthy statement over the weekend fully explaining the situation.
"We are of course devastated that this has happened and have done everything in our power to ensure it will not happen again," he said.
Noma norovirus outbreak - a timeline:
February 12-16 - A staff member who was carrying norovirus but was not showing symptoms unwittingly spread the disease, 63 out of 435 diners fell ill.
February 14 - A diner emailed the restaurant to say they had fallen ill. The email was picked up by a non-Danish speaker who passed the message on so it was not responded to until 18 February. The restaurant has since changed its internal procedures.
February 18 - Noma managing director Peter Kreiner spoke with the Health Department to put in a procedure to deal with the outbreak - the kitchen was thoroughly cleaned and all food touched during the affected period was disposed of.
This process was repeated three times over the next 48 hours.
All affected guests were offered a full refund or the chance to return to Noma as a guest of the restaurant. The majority of diners chose the latter.
February 20 - Noma was inspected by the Fødevarestyrelsen which was satisfied with the procedure and gave the restaurant the all-clear.
February 20 - One sink in the prep kitchen was found to have only lukewarm water, it was fixed immediately.
February 28 - Noma received a copy of the inspection report and placed it at the front of the restaurant, visible to diners as they enter.
March 1 - A link to the report was posted on the Noma website.
March 8 - A Danish news website posted a story with a link to the inspection's findings leading to a flurry of media interest in the story from across the world.
March 10 - Rene Redzepi posted a link to the Noma website and a lengthy statement on the story: "Dear friends thank you for your concern. Here are the facts! Best wishes Rene Redzepi and the entire Noma crew http://noma.dk/news/.