"The Russian football federation cannot organize matches in Crimea without the agreement of UEFA and Ukraine," said Infantino.
UEFA vice-president Grigoriy Surkis, who is also an honorary president of the Ukrainian Football Federation (FFU), said in a television interview that "the verdict shows that UEFA really cares about the development of football across the entire European continent."
Russia's Football Union (RFU) quickly confirmed it would comply with the ruling.
"We cannot ignore UEFA and FIFA decisions," RFU deputy chief Nikita Simonyan was quoted as saying by R-Sport news agency.
"We must comply with UEFA's decision as it's the European football governing body."
Ukraine's football federation meanwhile offered grudging support to the UEFA decision.
The decision "is not the best possible but optimal for the moment," Ukraine's Football Federation (FFU) spokesman Pavel Ternovoi said.
"The Crimean football clubs cannot play in any competitions without the FFU permission."
The strategic peninsula of Crimea, long home to Russian military bases, was annexed from Ukraine by Russia in March, sparking the worst crisis between Russia and the West since the Cold War.
The separatist uprising has cost the lives of over 4,300 people since April.
"Following the decision of UEFA's emergency panel on August 22nd, the executive committee decided to ban Crimean clubs from taking part in competitions organised by the Russian federation starting from January 1st 2015," said Infantino.
"Until a new order, Crimea will be considered as a special zone."
That would see UEFA financing development of football in Crimea, said Infantino, with the emphasis on youth football and infrastructure.
Since August 22nd, UEFA had already vetoed the participation of Crimea teams in Russian events before setting up a working group to present recommendations to the executive committee on Thursday.
Two Crimea teams who played in the Ukraine first division, Tavria Simferopol and Sebastopol have been disbanded.
But three sides — TSK Simferopol, SKCF Sevastopol and Zhemchuzhina Yalta — were quickly registered in the southern Russian cities of Krasnodar and Rostov-on-Don where they played in the Russian third division.