Chancellor Olaf Scholz is due to meet regional leaders on Friday to discuss how to respond to the spread of the highly-infectious Omicron variant.
"Tightening will unfortunately be necessary to counter the heavy wave that is coming our way," Karl Lauterbach told the RedaktionsNetzwerk Deutschland media group, without giving details.
Daily infections had been declining in Germany in December after the country introduced measures such as demanding proof of vaccination for many indoor activities, but they started rising again a week ago.
The Robert Koch Institute for infectious diseases reported 58,912 new infections on Wednesday, up 47% from a week ago. The country recorded another 346 deaths, taking the total to 112,925.
Lauterbach, a Harvard-educated epidemiologist, said current restrictions in Germany meant people had 50% fewer contacts than before the pandemic.
Finance Minister Christian Lindner was quoted as saying that Germany does not want to impose another lockdown.
"We want to avoid blanket and area-wide closures in the future," Lindner told the Stuttgarter Nachrichten daily and the Neue Berliner Redaktionsgesellschaft.
"Our goal remains to maintain social life as far as possible and to avoid social damage as far as possible."
Lauterbach said he wanted more than 80% of those who are fully vaccinated to receive a booster - or about 56% of the population: "The booster shot is the best protection from the Omicron variant," he said.
Germany has a relatively low rate of vaccination compared with other western European countries: 71.3% of the population is fully vaccinated and 39.3% have received a booster shot.
(Reporting by Emma Thomasson; Editing by Kim Coghill, Miranda Murray and Tomasz Janowski)
