The Foreign Relations Department said it is shocked that French President Nicolas Sarkozy said the festival should be used to draw attention to case of Florence Cassez.
"It is really surprising that a head of state would make a foreign policy decision that affects ties between two nations and governments in consultation with a person condemned by Mexican justice for a particularly serious crime," the statement said.
Tensions over the five-year-old case reignited last week when an appeals court upheld Cassez's conviction and 60-year prison sentence. Her lawyer and the French government say the case has been plagued with abuses, but the Mexican government insists her guilt has been proven.
Mexico "will not allow its artists and creators, or its businessmen and other participants in this program, to be exposed" to the furor over the Cassez case, the Foreign Relations Department said in a statement.
"Regrettably the government of Mexico will not be able to participate in the activities" of the festival, it added.
It was unclear how the Mexican government's refusal to participate would affect the "Year of Mexico" celebrations, which France launched last week. It features about 350 concerts, exhibits and other events throughout 2011.
Last week, French Foreign Minister Michele Alliot-Marie said she would snub the festival because of the Cassez case, but the French government has said it will not be canceled.
Cassez, who was arrested in late 2005, has acknowledged she lived at a ranch where the kidnap victims were held. But she said she was simply dating a Mexican arrested in the case and did not know the people there had been kidnapped.
Cassez's imprisonment became a hotly debated issue in France after Mexican police acknowledged they staged a televised raid of the ranch in which officers appeared to rescue the hostages and detain Cassez and a Mexican man. The Attorney General's Office acknowledged that, in fact, Cassez had been arrested the day before outside the ranch.
One of the victims identified Cassez's voice as that of one of her captors, and another suspect in the case said the Frenchwoman not only participated in abductions, but helped lead the gang that carried them out.
Her lawyer, Agustin Acosta, said the victims changed their testimony several times during the trial. He said that at first, three victims said they could not identify Cassez. But after the staging of the raid was discovered - two months after authorities first announced her arrest - two of the victims told police they could identify her, Acosta said.
In 2009, President Felipe Calderon rejected a request from Sarkozy that Cassez serve her sentence in France.
The Foreign Relations Department reiterated that stance Monday and insisted "the trial of Florence Cassez has demonstrated her guilt."