"The FBI is offering a reward up to $20,000 in exchange for information leading to the identification and arrest of this individual or group responsible for the attack," the mission tweeted.
The incident took place hours before US Vice President Mike Pence and first daughter Ivanka Trump arrived in Mexico City to attend the inauguration of Mexican President Andres Manuel Lopez Obrador.
Fox News reported earlier that the attack could have been ordered by a local kingpin from the Jalisco New Generation Cartel. It cited unconfirmed reports claiming cartel members had been ordered to attack US diplomatic missions.
The US government has initiated a new multi-agency program to destroy the powerful Cartel Jalisco Nueva Generacion (CJNG) drug-smuggling organization in Mexico.
The CJNG is considered responsible for trafficking many tons of cocaine, methamphetamine and fentanyl-laced heroin into the United States and for violence and significant loss of life in Mexico. It also operate sin Europe, Asia and Australia, according to the US Justice Department.
In 2015, members of the group attacked a military helicopter, killing eight people, and then a police patrol on one of the highways, killing 15 policemen and injuring another five. The casualties were among the largest for the Mexican police in recent years.