The initiative had provoked “a certain degree of irritation” among Germany's NATO allies, foreign minister Heiko Maas said.
Maas represents Merkel's junior, centre-left coalition partners the SPD, while Kramp-Karrenbauer is leader of the chancellor's conservative CDU party.
Turkey's military intervention in northeast Syria, as well as Russia's backing for the Damascus regime, mean “there are high hurdles for any internationalization of the solution to the conflict,” Maas said.
For now, the government “has engaged with efforts to resolve the conflict” with “diplomatic and humanitarian” means, he added.
There had been “no discussion” of an international mission to northeast Syria with Germany's allies, Maas said, recalling also the failure of a similar plan for northwestern Syrian region Aleppo in late 2016.
Kramp-Karrenbauer had told broadcaster Deutsche Welle on Monday that a “security zone” could allow international forces, including European troops, to “resume the fight against terror and against the Islamic State” group (IS) as well as “stabilize the region so that rebuilding civilian life is once again possible”.
The defence chief is keen to involve Bundeswehr (German army) soldiers, although a rare foreign deployment would have to be in line with international law and secure approval from parliament.
Europe and Germany must “come up with our own recommendations and initiate discussions,” rather than being “simply… an onlooker” Kramp-Karrenbauer said.
She added that she had already floated her proposal to the British, American and French defence ministers and would discuss it further at a meeting of the NATO alliance in Brussels on Thursday and Friday.
Kramp-Karrenbauer's call for military intervention came as Turkish President Recep Tayyip Erdogan was in Russia for talks with President Vladimir Putin on Syria.
Turkish forces are hours away from the end of a US-brokered ceasefire with Kurdish fighters in the offensive it launched on October 9th into the neighbouring country.
Ankara quickly moved to clear a “security zone” in northeastern Syria of Kurdish forces following President Donald Trump's announcement he would withdraw troops from the region.
The Kurds provided indispensable ground fighters in the US-led international coalition against IS, but their YPG militias are considered “terrorists” by Turkey.
Russia is a crucial ally of Syria's President Bashar al-Assad and has demanded that Turkey respect the country's territorial integrity.