The embassy received three letters on Thursday, one of which contained a powder, the RIA news agency reported.
Russia would also bolster its defenses after Finland, which shares a 1,300-km (800-mile) border with Russia, joined NATO.
The announced deal comes shortly after a similar deal for Israel to provide Finland with the David's Sling air defense system.
Moscow said it would keep a close eye on any NATO military deployments to Finland and respond accordingly.
Finland's announcement came immediately after admission to NATO was granted.
None of the five people Reuters spoke to sympathized with Finland's decision to give up its neutrality because of Russia's military campaign in Ukraine, also a neighbor of Russia.
Finland's accession roughly doubles the length of the border that NATO shares with Russia and bolsters its eastern flank.
Ben Berl Zyskowicz, who is the son of a Polish Holocaust survivor and a Finnish Jew, added that he was unfazed but felt the attack had dire meaning for democracy
Israel has, in recent years, ranked among the happiest nations in the world. Now, in 2023, it advances to the number four spot.