“Walter Haffner has been summoned to our (foreign) ministry where he has been made aware of our displeasure… The ambassador has been told those responsible must face justice,” the source said.
Several thousand people attended Saturday's rally called by Kurdish associations and Swiss political parties in Bern.
Ankara believes the Kurdistan Workers' Party (PKK), which Turkey dubs a terrorist group, was behind the rally where some people brandished a banner showing a gun pointing at President Recep Tayyip Erdogan's head alongside the words “Kill Erdogan”.
Erdogan criticised the Swiss for hosting the event, warning that “you will reap what you have sown”.
The Turkish leader has been angered by the refusal of several European states to allow Turkish ministers to campaign on the continent for a 'yes' vote in next month's referendum on expanding his powers.
Turkish Foreign Minister Mevlut Cavusoglu had on Saturday informed Swiss counterpart Didier Burkhalter of his country's anger over the march.
On Friday, Swiss prosecutors said they had opened an investigation into alleged spying on Turks living in Switzerland by an unspecified intelligence service after the attorney general's office cited “concrete suspicions” of espionage.
Burkhalter has previously voiced concerns about a crackdown in Turkey following a failed July coup against Erdogan that Ankara has blamed on US-based Islamic preacher Fethullah Gulen.