Pet owners will be given a choice: they must either neuter their tomcats, or keep them locked up or on a leash.
"It is necessary to limit or prohibit the free movement of male house and farm cats capable of reproduction for a limited time," a new Animal Welfare Report issued by the minister said.
"Either castrate your cat or don't let him out of the house," is the official advice to pet-owners.
Germany has about 1 million stray cats, according to government data.
In North Rhine-Westphalia, the country's most populous state, stray cats caused 500,000 ($817,850) of damage to flowers and trees last year.
The state had to introduce a ban on killing the strays after irate locals turned on them.
But despite the ban, which came into place in March, at least 1400 have been killed this year, according to the Green Party.
Authorities in the state have set aside 536,000 for neutering strays. But it is not just the damage to property that concerns the Government.
"Unlike wild animals, cats are a domesticated species that are not adapted to life without human support," a ministry spokesman said. "Without human care and support, the cats often experience considerable pain, suffering or harm."
Animal rights activists have spoken out in support of the minister's proposals. A spokesman for Peta described them as "an important measure against cat overpopulation, and to mitigate the suffering of homeless cats".
"Many feral cats are born small and sick, to a very miserable existence," Yvonne Wiegers, a local activist, told Schleswig-Holsteiner Zeitung newspaper.
The strays do not get vaccinations pet cats are given, and diseases are spreading rapidly in the wild population, according to the ministry.
