Andres Manuel Lopez Obrador, Calderon's political rival, had offered to lead Wednesday's protest but organisers said the protest should be nonpartisan.
Veronica Velasco, a Mexican television announcer, was the only speaker at the protest march. She called for "a new social pact" to increase jobs and wages and reduce Mexico's dependence on food imports.
Obrador held a separate rally, attended by many of the participants from the earlier protest.
Güncelleme Tarihi: 20 Eylül 2018, 18:16
On his weekly television show Obrador had urged people to join the march, saying: "We have to defend the people, because if we don't then who is going to do it?"
But march organisers were concerned that Obrador's involvement might turn the protest into a partisan debate and undermine the government's willingness to respond.
Obrador has disputed Calderon's legitimacy as president after Calderon won elections in July last year by less than one per centage point, proclaiming himself president of an "alternative government".
Servando Olivaria, a corn farmer and one of the marchers, said: "This is a spontaneous people's movement, with no political affiliation. Lopez Obrador can participate, but he should not head the march. He should not even speak about it."
Prices of tortilla, a staple food for Mexico's poor, have doubled over the last year to roughly 10 pesos ($0.7) per kilogram, due mostly to the surge in international corn prices.
One banner at the protest read "Calderon stole the elections, and now he's stealing the tortillas!"
Since taking office on December 1, Calderon has been criticised for failing to control the largest spike in tortilla prices in decades and is felt to favour agribusiness industries over the millions of poor in Mexico.
Calderon has said he does not want to return to the direct price controls enforced by many former presidents.
After the rally, in his own speech in Mexico City's Zocalo plaza, Obrador said: "Mexico needs a transformation of the magnitude of the [1910-1917] Mexican Revolution."
He demanded wage increases, subsidies and fixed prices for basic foods, and the cancellation of a clause in trade agreements that would lift restrictions on imports of corn and beans starting in 2008.
But some analysts feel Wednesday's protest shows how Obrador, who mobilised millions in support of his allegations that last year's election in July was rigged, has faded from the public's view.
Oscar Aguilar, a political analyst, said: "He used to have the money and influence to organise his own huge marches. Now he has to be a political opportunist and jump on someone else's train."