Mr Villiger had intended to be present at the service in the Bashkortostan capital Ufa, but cancelled the plan because his safety could not be guaranteed, according to a Swiss Government statement.
A total of 71 people died when two planes crashed in mid-air while under guidance from Swiss air traffic control on 1 July. The victims included 45 children from Bashkortostan.
At a separate memorial service at the crash site in Germany, Swiss Transport Minister Moritz Leuenberger admitted that Swiss officials had been wrong immediately to blame the Russian pilot for the disaster.
"The confrontation with the terrible notion of being part of the cause of the death of 71 people led us into helpless initial reactions, to confused and confusing information, to lapses," he admitted.
"Not everyone of us found the right words."
He told mourners at the ceremony in Ueberlingen, which was attended by German and Russian officials, that Switzerland was ready to offer compensation.
"Your pain is our pain, your suffering is our suffering," he said.
An investigation into the cause of the crash continues.
But the Swiss air traffic control company, Skyguide, has admitted that its collision warning system had been switched off for routine maintenance at the time and that one of the two air traffic controllers on duty had gone on a break.
Swiss 'warned'
The Swiss president's office issued a statement saying officials had been warned by the Russians that "emotions have been running high since Thursday evening in Ufa, and the safety of a Swiss delegation there on Saturday would have been endangered".
"President Villiger therefore is cancelling his already organised visit to Ufa," it added.
In Moscow, the Russian Foreign Ministry said the visit was being cancelled only because it could be clouded by outrage from grieving relatives.
Spokesman Alexander Yahovenko said: "The point is not that we cannot guarantee the safety of the Swiss president.
"The Bashkir authorities think that the ceremony will be very charged, full [of] serious emotional shocks.
"All of this, clearly, can have a negative effect on the atmosphere surrounding the Swiss president's stay."
Mr Villiger renewed his expressions of deepest sympathy towards the relatives of the victims, mostly children and teachers heading for a holiday in Spain.
Many of the relatives of those killed in the crash between the Bashkirian Airlines jet and the DHL Boeing have already visited Ueberlingen and there have also been emotional funerals in Ufa.