Sigmar Gabriel said 450,000 people had arrived in Germany so far this year, with 37,000 in the first eight days of September.
Tens of thousands, mainly Syrians, have pushed north in recent weeks.
Serbian TV says a record 5,000 migrants have arrived at the border with Hungary in the past 24 hours.
The Hungarian army earlier started military exercises to prepare for a possible future role in guarding the border and stem the flow of people – a move criticised by human rights groups.
Meanwhile, Austria’s government said 5,700 people had crossed over from Hungary in recent hours. National train operator OeBB temporarily suspended services from Hungary because of the increasing numbers and the risks of overcrowding.
A correspondent on the Hungary-Serbia border says refugees are being kept in a miserable, wet and muddy holding zone, with volunteers describing conditions there as a “disaster”.
Inclement weather conditions were also reported in northern Greece, forcing officials to allow at least 7,000 people, including many young children, to pass into neighbouring Macedonia.
On Wednesday European Commission President Jean-Claude Juncker announced plans to distribute 120,000 refugees from Greece, Italy and Hungary among member states via binding quotas.
This would be on top of a proposal in May to share 40,000 refugees from just Greece and Italy.
Speaking in the German parliament on Thursday, Mr Gabriel described the plans as “a first step, if one wants to be polite”.
“Or you could call it a drop in the ocean,” he added.
Thousands of migrants, many of them fleeing conflicts in countries such as Syria and Libya, continue to make the dangerous journey to Europe’s shores across the Mediterranean.
Another group of 2,500 migrants boarded a ferry hired by the Greek government early on Thursday to transport them from the island of Lesbos to the mainland.