A drug cartel has unleashed a campaign of violence in Jalisco state in response to the killing of one of its leaders last week.
Guadalajara, which will host four games at the finals as well as two World Cup play-off matches next month, is the state capital.
However, FIFA boss Infantino has given his complete backing to Mexico to host the matches safely and securely.
"Of course we are monitoring the situation in Mexico right now, but I want to say from the outset that we have total confidence in Mexico, in President Claudia Sheinbaum, in the authorities, and we are convinced that everything will turn out in the best possible way," Infantino told reporters while on a trip to Colombia.
"We have some matches in Mexico in a month for the play-offs; the new Azteca Stadium will be inaugurated. Mexico is a great country, a football country.
"As in every country in the world, things happen, which is why we have states, police and authorities who will ensure order and security. From my side, and from FIFA's side, I have absolute confidence.
"The authorities have more important things to talk about than football today, but football is part of Mexico and we are fully supporting President Sheinbaum, who shares that passion for football. Go Mexico and go with this celebration that will be for the whole world."
The president of the Colombian football federation Ramon Jesurun, whose national team play two games in Mexico including one in Guadalajara on June 23, said: "I'm happy to hear from the FIFA president.
"We remain delighted, pleased, and proud that our first two games will be there."
Jamaica are one of three countries set to take part in intercontinental play-off matches in Guadalajara next month, and the federation's president Michael Ricketts said on Tuesday that his organisation was still seeking assurances from FIFA and the continental confederation, CONCACAF.
