The annual arrivals were a record for Europe's biggest economy and around five times more than in 2014.
The number of Syrians seeking refuge in Germany last year hit 428,468, with Afghans the second-biggest group at 154,046, followed by Iraqis at 121,662.
Not all of them have yet filed official asylum requests, and not all will be allowed to stay as Germany has vowed to send back "economic migrants" from countries at peace.
The ministry also admitted that the 1.1 million figure may include repeated registrations in different German states, and people who have since moved on to other EU countries.
Actual asylum applications registered in 2015, amid a huge bureaucratic backlog, reached 476,649, the ministry said, more than twice as many as in 2014.
Only those fleeing war - such as Syrians, Iraqis and some Afghans, who together make up around half of applicants - have a high likelihood of being granted refugee status.
Chancellor Angela Merkel has made clear that most citizens of Balkan states such as Serbia, Albania and Kosovo would be repatriated.
Interior Minister Thomas de Maiziere on Wednesday reiterated the government's determination to end the trend of increasing arrivals of asylum seekers.
"We will work in all policy areas towards sharply reducing the number of new asylum seekers to Germany," he said.
Arrivals in December had dropped from an autumn peak, but de Maiziere put that down partly to stormy weather that dissuaded would-be migrants from embarking on the perilous journey across the Mediterranean.
He pointed instead to what he described as a worrying trend of increasing Moroccan and Algerian arrivals in December.
The number of Moroccan asylum seekers reached 2,896 in December, making them the fifth biggest group of applicants, noted de Maiziere, adding that "Algerians are just behind".
"That's obviously cause for concern and we will take care of it," he said, adding that the government would examine "what is behind this and what one can do there".
The record migrant influx has split public opinion in Germany, and Merkel is increasingly coming under fire, even in her own coalition, for her open-door stance to those fleeing war and misery.