It is the largest outbreak of this variant in the northern European country, Bente Moller of the agency responsible for patient safety told the Ritzau news agency on Saturday.
Those infected were mostly staff and guests at a restaurant in the Nordsjaelland area north of the capital, Copenhagen.
However, they had also infected other people.
The authorities have not classified the outbreak as particularly dangerous.
The variant does not differ from the original virus.
It is not yet known how the variant from Mexico entered the country.
The Danish government and a broad majority in parliament in Copenhagen had agreed in March on a comprehensive reopening plan to gradually reduce restrictions on public life.
So far, nearly 1.5 million people in the EU country have received a first Covid-19 vaccination, which is about a quarter of the population.
Almost 800,000 people have been injected with the second dose needed for full protection.