The institute said several Mexican mobile phone carriers, including market leader America Movil, must pay a fine of about $104,000 and stop using "iPhone" as a promotional name for their calling plans.
But Apple is not specifically covered by the ruling, since it doesn't provide calling services, just handsets. Apple had previously argued the Mexican firm's trademark had lapsed.
The ruling can be appealed, but the institute said about 68 percent of its rulings are upheld on appeal.
Previous reports suggested the Mexican company might sue Apple for as much as $1.5 billion trademark infringement, but iFone executives did not return calls for comment on whether they planned to file any civil suit.
It's not the first time Apple has faced disputes over the name.
In 2013, Brazil's patent authority ruled the iPhone name in Brazil belongs to a local company called Gradiente SA. The verdict didn't forbid the global computer giant from using the name in Brazil.
Gradiente was the first to make cellphones in Brazil, and launched the first national smartphone in 2004. Their request to use the iPhone trademark was granted in 2008, and the company started making 'iphones," with a lowercase 'p' .
The issue is reminiscent of one that arose in the United States in 2007. Cisco Systems had owned the iPhone trademark since 2000, and had been using it for a line of Internet-connected phones.
Once Apple announced its intention to use the brand name, Cisco sued it in San Francisco federal court. The two companies settled out of court six weeks later, without disclosing the terms.