The decision will come into force on Friday and be announced by the national health body, the Robert Koch Institute, according to the daily newspaperFrankfurter Allgemeine Zeitung.
Covid-19 incidence rates, which measure the number of infections recorded for every 100,000 people over the previous seven days, have crossed the threshold of 200 in numerous French departments.
In the region surrounding Paris, the figure has exceeded 600.
"While we see such a high incidence it is simply a necessity... a practically automatic process," Chancellor Merkel told a press conference in Berlin on Thursday as part of an EU summit focused on the fight against Covid-19.
"It is not related here to a political decision but, when we see the evolution of the incidence rate -- as is the case here -- exceed the threshold of 200 for a long time, that requires a classification as a zone of high risk," she added.
France to join Austria's Tyrol, Czech Republic
Up until now, only France's border area of Moselle had been classified by Germany as a high-risk zone.
The classification imposes several travel restrictions, including a requirement to obtain a negative test result before entering German territory, a ten-day quarantine, as well as the imposition of strict border controls.
Berlin has also placed Austria's Tyrol state and the entire Czech Republic in the same high-risk category.
Chancellor Merkel has hinted that France could enjoy special treatment and avoid strict border controls, despite being classified as a high-risk area.
"There is a whole specific test procedure... that is in discussion with France," she said.
The French secretary of state for European Affairs, Clément Beaune, "is negotiating the easing of terms... to avoid the border being closed," according to the AFP news agency.
