Defence Minister Annegret Kramp-Karrenbauer said the question of sanctions on the pipeline, which will bring gas from Russia to Germany, rested on Moscow's cooperation in clearing up what exactly happened to Navalny.
Foreign Minister Heiko Maas said suspicion would fall on Russia if it failed to help resolve the matter.
Navalny was airlifted to Germany for hospital treatment after falling ill on a Russian domestic flight last month. The German government says he was poisoned with a Novichok nerve agent similar to the one used in an attempt to kill a former Russian spy in England two years ago.
Moscow says it has seen no evidence he was poisoned.
"I have always said that I am not fond of the Nord Stream 2 project," Kramp-Karrenbauer said. "To me it was always clear that the security interests of Eastern European states and Ukraine must be taken into consideration."
Pressed on whether Germany was ready to sanction the project, Kramp-Karranbauer said: "What happens now depends on the behavior of the Russian side."
Foreign Minister Maas of the Social Democratic Party (SPD), junior partners in Merkel's coalition government, said in remarks published on Sunday that a failure by Moscow to help to clear up the circumstances of Navalny's illness would add to suspicions that Russia's government was involved.
"I certainly hope that the Russians will not force us to change our position on Nord Stream 2," he told the Bild am Sonntag newspaper.
The affair has led to calls from several leading conservatives for Merkel to suspend the pipeline, a huge, nearly complete project to bring Russian gas to Germany under the sea.Merkel, a supporter of the pipeline, has said it should not be linked to the Navalny case.