The European governing body has already charged the Russian club with the "racist behaviour of their fans" after Manchester City's Toure complained of monkey chants directed at him during the Champions League match on Wednesday night.
UEFA issued another statement on Friday which read: "Further to the opening of disciplinary proceedings against CSKA Moscow following the alleged racist behaviour of some of their supporters at the UEFA Champions League match between CSKA and Manchester City FC on 23 October, UEFA president Michel Platini has requested that the UEFA administration immediately conduct an internal investigation to understand why the three-step protocol established to deal with incidents of a racist nature was not implemented."
Under UEFA rules, the referee is allowed to stop the match and ask for an announcement to be made urging spectators to stop such racist conduct and warn that the game will be suspended and subsequently abandoned should such behaviour continue.
On Wednesday, though, no announcement was made and the match continued.
UEFA said it would publish the findings of its investigation once the disciplinary case against CSKA had been dealt with by its independent control and disciplinary body on October 30.
The Russians have denied any racist abuse took place, saying they were "surprised and disappointed" by the allegations.
A "furious" Toure raised the prospect of a boycott of the 2018 World Cup in Russia following the match and has been backed by anti-racism campaigners.
RIA Novosti quoted the Ivory Coast midfielder as saying: "If we aren't confident at the World Cup, coming to Russia, we don't come."
Piara Powar, executive director of European anti-discrimination body FARE and a FIFA anti-discrimination task force member, said Toure was right to raise the issue of the 2018 World Cup.
Powar told Press Association Sport: "Yaya Toure is absolutely right in raising the spectre of African players or players of African heritage not going to the 2018 World Cup - and without them there will not be a World Cup in Russia.
"I wouldn't blame them - in this era players are the most powerful force and if all the players said they are not going there wouldn't be a World Cup, or if there was it would be meaningless."
Powar said he did not envisage racism at a World Cup in Russia but that the situation in Russian club football was "dire" and fuelled by far-right extremists.
FARE has identified banners supporting the Greek far-right political party Golden Dawn - which has a swastika-like symbol - being displayed in several stadiums in eastern Europe including Romanian grounds and in Moscow on Wednesday.
Match referee Ovidiu Hategan from Romania has come in for criticism for failing to follow UEFA's procedures.
PFA deputy chief executive Bobby Barnes, who is also European president on the international players' union FIFPro, said: "We're very disappointed that a clear agreed protocol which is designed to deal with these situations was not effected.
"The player, having done what was asked of him to notify the referee, quite rightly expected that the referee would go speak with the safety officer, and the (UEFA) protocol agreed is that the safety officer should make a stadium announcement warning the fans that if the chants do not desist that the game will be stopped."
City manager Manuel Pellegrini did not want to add much more to the club's official stance, insisting it was now a matter for UEFA.
"I talked with Yaya, he is okay," he said.
"I think Yaya did the right thing to say what happened and we will see what UEFA will do about it.
"UEFA is doing a special campaign against the racists and I think they do the right things for the future not to repeat it, but I don't know what they are going to do."
On Platini's intervention he added: "UEFA must take their decision about that. We did all that we can do here, we can't do any more."
Pellegrini, who admits he only learned of the allegations of racist abuse at the post-match press conference, would not be drawn on Toure's suggestion players should boycott the 2018 World Cup in Russia.
"I repeat we must wait for UEFA," he said.
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