CSKA Moscow were ordered by UEFA to play a 2013-14 Champions League game behind closed doors after Manchester City players were racially abused by their fans.
It was one of more than 200 discriminatory incidents involving Russian clubs in the past two years, according to the Moscow-based SOVA Centre and the Football against Racism in Europe network.
While controversy reigns over the troubles in Ukraine, and question marks remain over the construction of the 12 competition venues, Valcke, 54, is most concerned with the country's social problems.
"The real worry we have in Russia is racism and discrimination," Valcke explained.
"When you see what happens in Russian football. ... We have to find solutions with the authorities and the organising committee.
"We can't allow ourselves, as a general rule, to have such incidents, but even less so during a World Cup match. That's my biggest worry."
The state of readiness of the 12 tournament venues is also proving a headache.
Three of the stadia are ready, including Spartak Moscow's state-of-the-art Otkrytie Arena, but those in Rostov-on-Don, Nizhny Novgorod and Saransk have been delayed while construction in Kaliningrad will only start this summer.
Sanctions imposed on Russia by the international community as a consequence of the conflict in Ukraine has made building work all the more difficult.
The tournament will be the most expensive yet held even if its total budget was recently reduced to 637.6 billion rubles (€11.5 billion).
"The current economic situation is not going to change everything," Alexey Sorokin, CEO of the 2018 local organising committee, told L'Equipe. "The majority of contracts have already been signed, the provisional cost of the stadia was calculated in rubles, so the impact will be limited.
"Concerning imports, our government has taken steps. In certain cases, we're going to local materials as a substitute. Certain taxes are going to be reduce for products that we still need to import."
He added: "Two stadia, Yekaterinburg and Kaliningrad, are a little bit behind schedule due to a change in capacity. We have to look again at their design, which has pushed the deadline back. But we're convinced all the stadia will be finished by autumn 2017."
