Dobrindt, who is a member of the Chancellor Angela Merkel's conservative Bavarian allies CSU, warned that the country "has reached its limit of capacity", a day after 12,200 more refugees reached Munich -- a key arrival point.
Police warned on Sunday that Munich is at the limit of its capacity to welcome refugees arriving en masse.
"We had a total of 12,200 refugees on Saturday... today we're expecting several hundreds. Given the numbers from yesterday, it is very clear that we have reached the upper limit of our capacity," said a police spokesman.
"Our aim today would be to transport as many as possible out of here, to make place for new arrivals," he said.
Munich has become a key arrivals point for refugees travelling to Germany by train through Hungary and Austria.
Last weekend, about 20,000 migrants arrived at the city's main railway station.
The president of the Upper Bavaria region, Christoph Hillenbrand said he did not know "how we can cope", according to the Bild am Sonntag tabloid which headlined its article "Munich at the brink of collapse".
Bavarian public television BR said the city "came very close to a humanitarian disaster", although authorities managed to limit the numbers of people sleeping on mattresses on the floor to just a few dozens, rather than the hundreds as earlier feared.
Authorities are mulling whether to open up the Olympiahalle -- a stadium used for the 1972 Olympics and which today serves as a concert hall or sports arena -- as a temporary shelter for the refugees.
As Germany buckles under the strain of the record refugee influx expected to reach 800,000 this year, dissenting voices from the CSU have grown louder.
Dobrindt's statement came just days after CSU vice president Hans-Peter Friedrich called Merkel's decision "an unprecedented political error" that would have "catastrophic consequences".