It was a joyful ceremony when Sheinbaum was sworn in before hundreds of Mexican congress members.
“Presidenta, presidenta”, the feminine form of the word president in Spanish, was heard among the cheers.
The 62-year-old Sheinbaum received 60 percent of the votes in the presidential election in June, while the closest challenger Xóchitl Gálvez had to settle for just over 25 percent.
In her speech, she highlighted the significance of her election victory for the women who have fought to make their way in Mexico.
Including those who dreamed of the possibility that one day, regardless of whether we were born as women or men, we could realize our dreams without our gender determining our fate, she said.
She also promised to limit prices on food and gasoline, increase business investments, and build more homes and passenger trains.
The drug cartels, which control large parts of the country, were briefly mentioned at the end of the speech.
The new president also faces a range of other challenges, such as a weak economy, unfinished construction programs, and growing debts.