"We are dealing with exponential growth," Altmaier told a German-French economic conference via video link in Berlin. "In Germany the number of new infections is rising by 70-75% compared to the week before."
Altmaier's forecast shows that Germany is contending with a faster upswing in coronavirus cases than previously expected. At the end of September, Chancellor Angela Merkel said there could be 19,200 cases per day by Christmas.
On Tuesday, the number of confirmed coronavirus cases rose by 11,409.
Merkel and leaders of Germany's 16 states will meet on Wednesday to decide on additional restrictive measures to slow the second wave of the pandemic.
Daily Bild reported the Chancellor is planning a "lockdown-light" which would mainly focus on the closure of bars and restaurants to try to contain the spread of infections.
Altmaier said rising infections across Europe and corresponding curbs on daily life would make it harder for economic growth to rebound as quickly as previously hoped.
But he did not expect supply chains to be disrupted like they were during the first wave of the virus in spring.
The German government expects Europe's largest economy to shrink by 5.5% this year, a source told Reuters on Monday, a slightly more optimistic forecast than its previous guidance for a 5.8% decline in gross domestic product.