Germany's response measures included the closure of a Russian cultural centre in Berlin and a consulate in Bonn. On Tuesday, President Vladimir Putin accused Germany of planting evidence in order to blame Moscow for the incident.
Lavrov said Russia would close the centres in the cities of Moscow, St Petersburg and Yekaterinburg, after Germany's decision to halt the operation of the Russian centre in Berlin.
"They (Germany) deliberately took this step - they could not have failed to understand - which means the end of their cultural presence in Russia," Lavrov said, according to state news agency TASS.
The centres had stayed open "despite all the Ukrainian complications in our relations with the West," he added.
Russia's first Goethe-Institut opened in Moscow in 1992, soon after the collapse of the Soviet Union. Following a diplomatic spat with Britain, Russia ordered the closure of its British Council in 2018.
Lavrov's deputy, Alexander Grushko, said Russia would retaliate "very soon" for the closure of the Bonn consulate.
Moscow has been widely accused by Western officials of running a campaign of sabotage and disruption with the aim of undermining support for Ukraine and destabilising European nations.
Russian President Vladimir Putin has dismissed the allegations, saying Berlin wants to distract from its own failings and dissatisfaction among voters.
Any proof being offered "has been planted," Putin said.
European Union ministers on Wednesday weighed how best to respond to the attempted drone attack but struggled to find new ways to meet the challenge without resorting to military means.
"It is clear that it has all the hallmarks of state-sponsored terrorism. The question is: what do we do about this," EU foreign policy chief Kaja Kallas told reporters before a meeting of the bloc's foreign ministers in Ireland. The ministers discussed sanctions, visa restrictions and shutting Russian consulates, among other measures.
The EU has slapped almost two dozen packages of sanctions on Russia over the war in Ukraine, hitting more than 3000 officials, oligarchs and entities including banks, energy companies and drone makers.
The EU was already preparing to impose more travel bans and asset freezes on another 1600 people, Kallas said.
with AP