Czech Republic placed on the list of high-risk areas

The Robert Koch Institute (RKI) puts countries with an increased risk of becoming infected with SARS-CoV-2 on a list of high-risk areas. Due to rising numbers of new cases in the Czech Republic, where the R number is over 50 per 100,000 inhabitants, as of September 23, 2020 Germany classified the entire Czech Republic except for the Ústí nad Labem and Moravia-Silesia regions as a high-risk area. 

General consequences in Germany

Anyone who has been in a high-risk area in the 14 days before entering Germany is still required to go into home quarantine immediately upon arrival until they can provide a negative test. The test results must be presented upon request at the relevant public health authority. Travellers arriving from high-risk areas must submit themselves for testing and inform the relevant public health authority immediately. Exceptions still apply for transit, absolutely necessary and unavoidable trips for business or medical reasons, cross-border movement of persons, goods and freight for work reasons or for persons who spent less than 48 hours in the high-risk area or who have another serious reason.

Each federal state issues its own detailed quarantine regulations.

Bavaria: The current quarantine measures remain in place until October 3, 2020. For more on the provisions currently in place, please see the Newsalert dated September 10, 2020. 

https://www.gesetze-bayern.de/(X(1)S(cyb1xj2snmpsl4mftic3yqii))/Content/Document/BayEQV/true?AspxAutoDetectCookieSupport=1%20 

Saxony: The current quarantine measures for Saxony as updated on September 10, 2020 remain in place. For more on the provisions currently in place, please see the Newsalert dated September 10, 2020.

https://www.coronavirus.sachsen.de/download/SMS-Saechsische-Corona-Quarantaene-Verordnung-2020-06-25-Konsol-Lesefassung-2020-09-11.pdf 

UPDATE: Other information concerning Germany

Free testing: The option for travellers coming from areas that are not high risk to undergo free testing ended on September 15, when summer travel ended. Only Bavaria offers free testing until at least October 1, 2020. After September 15, 2020 travellers who have been in high-risk areas in the previous 14 days are entitled to a free test upon entering the country.

Extended quarantine: After October 1, 2020 travellers from high-risk areas will probably be able to come out of home quarantine after undergoing testing no sooner than five days after entering the country. The federal government and federal states are also discussing whether to introduce a mandatory five-day quarantine for travellers returning from high-risk areas. 

UPDATE: Austria

As of Monday, September 28, 2020, at midnight, Austria will issue a partial warning against travelling to Prague (warning level 5). Austria is warning against travelling to this region as of September 28, 2020 due to the increased risk of coronavirus infection (COVID-19).
Travellers coming from the above-mentioned high-risk areas must present a negative PCR test no more than 72 hours old upon entry to Austria or go into home quarantine for 10 days. If travellers cannot provide a negative test upon entry, they must request a test in Austria within 48 hours. If the test comes back negative the quarantine will end early. Exceptions 
to these measures apply for regular cross-border workers (pendlers with confirmation from their employer), people travelling for important family reasons and cross-border movement of goods and passengers. 

For more information, please see: 

https://www.sozialministerium.at/Informationen-zum-Coronavirus/Coronavirus---Haeufig-gestellte-Fragen/FAQ--Reisen-und-Tourismus.html 

https://www.ris.bka.gv.at/GeltendeFassung.wxe?Abfrage=Bundesnormen&Gesetzesnummer=20011194