Rivera is a former telenovela actor, and critics have long charged that the photogenic couple's marriage was a marketing strategy to burnish Pena Nieto's image for his 2012 presidential campaign.
Earlier this week the magazine Hola reported that the couple had split in December; Pena Nieto's six-year term ended Dec. 1.
In a brief message published on social media, Rivera said she had always given her all to the marriage and deeply regrets "this very painful situation."
"Today all my energy, strength and love are focused on continuing to be a good mother, on recovering my life and my professional career," Rivera said.
In 2014, many Mexicans were outraged when it was reported that Rivera was living in a multimillion-dollar home registered to a builder that had been awarded public contracts.
She said at the time that she had been purchasing the mansion legitimately with earnings from her acting career, but that she was selling her stake in the property.
Rivera and Pena Nieto's last official public appearance together was Sept. 15 for Mexican Independence Day celebrations. They were also seen in January at the funeral of a prominent leader of his Institutional Revolutionary Party.
According to Hola the two remain "cordial," and while Pena Nieto and his three children are still in Mexico, Rivera and her children have gone to her residence in the United States.
Pena Nieto and Rivera, known as "La Gaviota" or "the seagull" for a character she played on a soap opera that brought her fame, wed in 2010 when he was governor of Mexico State. It was the second marriage for each.