Oseguera, known as "El Mencho" and mastermind of the powerful Jalisco New Generation Cartel (CJNG), died in custody after being injured in a special forces operation on Mexico's Pacific coast in Jalisco state, according to the defence ministry.
"At FIFA Mexico, we are closely monitoring the situation in Jalisco and remain in constant communication with the authorities," a FIFA spokesperson told Reuters.
"We will continue to follow the actions and directions from the different government agencies, aimed at maintaining public safety and restoring normalcy, and we reiterate our close collaboration with federal, state, and local authorities."
Estadio Akron in Zapopan, Guadalajara, is one of three Mexican venues set to host World Cup matches this summer. The stadium will also host playoff matches between Congo, Jamaica and New Caledonia from March 26-31.
The Mexican league said on its social media pages that two top-tier games scheduled for Sunday - Queretaro vs FC Juarez in the men's league and Chivas vs Club America in the women's league - had been postponed indefinitely. Two second division matches scheduled for Sunday were also called off, local media reported.
Sunday's women's match between Necaxa and Queretaro in Aguascalientes was suspended when players fled the pitch after hearing loud noises outside Estadio Victoria, which media reports described as gunshots. The match later resumed, with Necaxa winning 2-1.
The Mexico national team is due to face Iceland on Wednesday in a friendly fixture at the Corregidora Stadium in Queretaro.
After reports of El Mencho's death, suspected cartel members blockaded highways with burning cars and torched businesses in more than half a dozen states. No civilian deaths were reported.
In Jalisco's popular beach resort of Puerto Vallarta, frightened tourists on social media described plumes of dark smoke rising into the sky from around the bay.
Air Canada, United Airlines, Aeromexico and American Airlines suspended flights in the area.