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Lauterbach is self-isolating at home while continuing to conduct official duties. Germany is likely to reintroduce measures to prevent the spread of the coronavirus in winter.
"The minister is fine, he has only mild symptoms. He is temporarily conducting his official duties from home isolation," the German Health Ministry said.
Lauterbach, 59 and a Social Democrat member, has received four doses of the COVID vaccine. The ministry said this "shows that with the highly contagious omicron variant, infection cannot be completely ruled out, even with extreme caution."
"The minister therefore again appeals to everyone to behave prudently and pay attention to adequate vaccination protection, so that infections and severe cases can be prevented as much as possible."
On Wednesday, the German government announced basic COVID measures, only a few of which are applicable nationwide, with a much greater focus on allowing states the rights to choose what to implement. The most notable national plan, the compulsory wearing of face masks on long-distance trains and airplanes, will remain in place during upcoming fall and winter.
A negative COVID-19 test will also be required from October until early April for many people to secure entry to hospitals, nursing homes and similar institutions with vulnerable people. The government statement was not clear on whether this would also include staff, but did indicate that people who were recently vaccinated or infected and recovered would likely be exempt.
However, Germany's 16 states are largely left to implement their own rules from among a range of options depending on how severe the situation becomes locally. State governments could decide to require masks on local public transport, in schools for students, or at indoor events, for example.
Schools, prisons and shelters for asylum-seekers may implement regular testing if infections rise, Germany's health and justice ministers said in a joint statement on Wednesday.
The government also plans a vaccination drive in the coming months in the hope of keeping infection numbers down.
"Germany should be better prepared for the next coronavirus winter than in previous years,'' Health Minister Karl Lauterbach said earlier this week.
Justice Minister Marco Buschmann said he was keen to keep schools open, while states will "only be able to impose a mask requirement at schools if this is necessary in order to be able to continue to provide in-person teaching."
"Children have a right to school education and a school day that is as carefree as possible. School closures must therefore not be allowed," Buschmann said.
The new rules still need to go to the cabinet and parliament for approval, though this is expected to be a formality.
jsi/msh (AFP, dpa, Reuters)