Carlos Abascal, the interior minister, said Fox will instead give the highly-charged cry of independence in the central town of Dolores Hidalgo.
The conservative Fox has been targeted by protesters angry at what they say was fraud in July's presidential election which was narrowly won by Felipe Calderon, the ruling party candidate.
The traditional ceremony, known as "el grito" (the shout) takes place on September 15, the eve of independence day in the capital's huge Zocalo square, but leftist protesters who have occupied the plaza for weeks had vowed to demonstrate against Fox there.
Mexico's Senate urged Fox to take the event elsewhere.
Abascal said: "The federal government accepts the Senate's request today to consider a change of venue."
Andres Manuel Lopez Obrador, the leftist candidate, who says he was robbed in the election, plans to hold his own independence ceremony in the Zocalo on Friday night cheered on by tens of thousands of supporters.
The move to Dolores Hidalgo, where national hero Miguel Hidalgo kicked off a struggle in 1810 that led to Mexico's independence from Spain, represented a retreat by Fox.
The president's spokesman had repeatedly insisted Fox would lead the ceremony in the Zocalo, once the centre of the Aztec empire and now the heart of modern Mexico.
Leftist politicians who seized the podium of Congress forced Fox to abandon his state of the nation speech on September 1. He later gave the address on television.
The change of plan for "el grito" reduces the risk of violence in a country divided between left and right only six years after Fox ended decades of one-party rule.
Leftist protesters wound down a huge sit-in protest on Thursday that had crippled the centre of the capital.
Leftists will decide in coming days whether to keep up a campaign of civil resistance against Calderon, who won by 234,000 votes out of 41 million and takes office on December 1.
The six-week sit-in caused traffic chaos in the already congested city and devastated business in Mexico City centre.