Swiss envoy Yves Rossier was told such “confrontational rhetoric” could seriously harm otherwise constructive ties between the two countries, Moscow's foreign ministry said.
A separate statement said Dutch ambassador Renee Jones-Bos had been summoned in connection to a media “campaign to whip up spy mania”.
Swiss officials have said that Russian agents launched separate cyber attacks on the Spiez laboratory in Bern and the Lausanne office of the World Anti-Doping Agency (Wada).
The lab, which does analytical work for the Hague-based Organisation for the Prohibition of Chemical Weapons (OPCW), was investigating the poisoning of Russian double agent Sergei Skripal in Britain.
Wada for its part has been a thorn in Moscow's side for several years over drug cheating in Russian sport.
Dutch officials and media reports said the spies were arrested in the Netherlands and then expelled.
Swiss foreign minister Ignazio Cassis is due to meet with his Russian counterpart Sergei Lavrov in New York next week over the spat.