"However, the border crossings that people stormed while trying to illegally enter the United States will be reinforced", the ministry said.
Tijuana's municipal government said that more than three dozen migrants were arrested for disturbing the peace and other charges related to the march and what followed.
A group of Central American migrants, mostly Hondurans, climb a metal barrier.
Authorities on the US side used tear gas to disperse the would-be crossers, the journalists told CNN.
But amid the stinging gas, several migrants turned back. A federal judge has at least temporarily ruled against the policy, but the administration has taken steps to harden the border.
More than 5,000 migrants and refugees have gathered in Tijuana in the past week with the hope of entering the US. It is said to be the busiest port of entry in the Western Hemisphere, CNN reported.
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Some saw an opportunity to breach the crossing. Close to 3,000 migrants took Mexico up on the offer.
Children screamed and coughed in the mayhem of the tear gas.
Although the number of people in the caravan was relatively small, the unrest, with migrants attempting to climb fences and run through auto lanes to reach the US, and scenes of mothers and children choking on tear gas, represented a serious escalation of the caravan crisis.
As the chaos unfolded, shoppers just yards away on the USA side streamed in and out of an outlet mall, which eventually closed.
People attempting to cross into the US.
Department of Homeland Security Secretary Kirstjen Nielsen said in a statement that USA authorities will continue to have a "robust" presence along the Southwest border and that they will prosecute anyone who damages federal property or violates US sovereignty.
"As I have continually stated, DHS will not tolerate this type of lawlessness and will not hesitate to shut down ports of entry for security and public safety reasons", Nielsen said.
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Thousands of additional migrants are also expected to arrive in Tijuana.
The San Ysidro crossing is a large complex with multiple lanes of vehicle and pedestrian access points. We will close the Border permanently if need be.
"People had thought that they were going to open the gates, but that was a lie", Caballero said.
Amnesty International said what happened Sunday was predictable after Trump ordered the troops to the border and said he told them that if a migrant throws a rock, "consider it a rifle".
"Would be very SMART if Mexico would stop the Caravans long before they get to our Southern Border", Trump wrote on Twitter on Sunday.
"Mexico should move the flag waving Migrants, many of whom are stone cold criminals, back to their countries", Trump tweeted. US border officials have said they have a limited capacity to process asylum seekers, up to 100 per day. "Congress, fund the WALL!" he added.
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The Mexican Interior Ministry said Sunday that since October 19, it had sent almost 2,000 Central Americans who were part of recent caravans back to their countries. The Mexican government described Sunday's events as "acts of provocation" that were "far from helpful" for the migrants' objectives.