"These illegal acts were clearly attacking our national security, committed by true traitors who have no respect for others or for the country, Calderon said.
"Those who believe they can use fear to hold our society hostage and immobilise us, are mistaken. ... They are doomed to fail."
The two grenades exploded simultaneously, about 500 metres apart, during the traditional "grito," or shout for independence, in Morelia's main plaza late Monday night.
Morelia is the capital of Michoacan, Calderon's home state, which has been increasingly hit by drug-gang violence in recent years.
Leonel Godoy, the governor of Michoacan, who was leading the ceremonies, said witnesses saw a man wearing black throw one of the grenades and beg forgiveness for what he had done.
But he provided no more details, and there were no immediate claims of responsibility.
The governor of Michoacan cancelled a march in Morelia after the grenada attacks [AFP]
"Without a doubt, we believe this was done by organised crime," he said.
But Mexicans are fearful of more attacks.
"This is not going to stop. This is only going to get worse," said Arevalo, a cooking student.
"Up until now the killers have targeted other drug traffickers, but now it seems we're going to see still more violent acts against everyday citizens, just to shock people."
But others expressed defiance.
"Mexico is ours. We won't hide. We are going to go out and take back our streets," said lawyer Juan Enrique Arguijo, 46.
Godoy cancelled Tuesday's march in Morelia after his office received threats, "because there are children, women and innocent people who have been hurt."
More than 2,700 people have been killed in Mexico in violence related to the drugs trade this year as cartels fight an army crackdown ordered by the government.
Warfare between rival gangs has also increased.
El Universal quoted Juan Jose Rosales, a local TV journalist, as saying: "First one person went down and then it was like domino pieces."
Police could not immediately say whether drug gangs were behind the blast, but if so it could be their most brazen attack yet, hitting Mexico's biggest annual street party.
September 15 is celebrated in Mexico as independence day, when Miguel Hidalgo, a Roman Catholic priest, launched a revolt against Spanish rule in 1810 by ringing a church bell and shouting "Viva Mexico" to a cheering crowd.
The first explosion in Morelia went off during a re-enactment of the bell-ringing.
The attack comes only days after 24 bodies were found bound and killed execution-style in a rural area outside Mexico City in one of the largest massacres in recent history.