But in a statement on social media on Monday it said: "We have a longstanding practice of applying name changes when they have been updated in official government sources."
It will also rename Mount Denali as Mount McKinley in the US, following another order from Trump.
"When official names vary between countries, Maps users see their official local name," it said.
Sheinbaum has criticised Google's decision, saying the firm should not respond to "the mandate of a country" to change the name of "an international sea".
But she seemed to poke fun at Trump's move by joking Mexico may demand Google make some additional renaming decisions.
"By the way, we are also going to ask for Mexican America to appear on the map," she said.
Sheinbaum previously joked she would consider renaming North America as "América Mexicana" in the country.
"He says that he will call it the Gulf of America on its continental shelf," Sheinbaum previously said when Trump signed the executive order.
"For us it is still the Gulf of Mexico, and for the entire world it is still the Gulf of Mexico."