Pena made the claim on Argentine streaming channel Luzu TV following Argentina's opening group game win over Algeria.
I don't want to bring bad news, but Messi's father has just passed away. It was sudden. In the middle of the World Cup,
The report quickly spread on social media before Pena clarified that the information had not been confirmed.
The Messi family later issued a statement confirming that the player's father, Jorge Messi is receiving medical treatment for an undisclosed health condition. The statement said the 68 year old is under medical supervision and recovering, while criticising speculation surrounding his health and calling for privacy during a difficult period.
Pena apologised publicly and said the information had been passed to her during the programme as if it was verified news.
I apologise to the Messi family. I am deeply ashamed to have been involved in this mistake.
The 51 year old television personality and actress now says she was given unverified information.
I have to clarify that this false information was given to me live on air as if it had been checked by the show's production team, and I trusted it. Even so, I take responsibility for being part of the mistake and that is why I decided to step aside and end my participation in Luzu. I apologise again from the heart; I was wrong.
Luzu TV also apologised and announced disciplinary action following the incident, saying the dissemination of sensitive information without proper verification was unacceptable.
Nicolas Occhiato, the show's host and producer, said:
We at Luzu TV deeply regret what happened on the air during the program El Show de Verano. For our channel, the broadcast of sensitive information without proper prior verification is unacceptable. For this reason, Luzu TV management has decided to terminate the employment of all those responsible, and Florencia Pena has decided to step down. We reaffirm our commitment to responsible, respectful, and rigorous journalism.
The controversy came after Messi scored a hat trick in Argentina's 3-0 win over Algeria. The 38 year old appeared emotional during the match and later said he had experienced difficult days for personal reasons unrelated to football.
The false report triggered widespread criticism across Argentina, with many supporters condemning the failure to verify the information before it was broadcast.
Argentina's President Javier Milei called it trash talk on X, saying that Pena's outrageous and unscrupulous, unverified statements on a streaming channel, which would still be outrageous even if the information had been true, since they concern a citizen's private life, remind us of the impunity with which some individuals believe they can operate simply because they have a microphone or a pen in their hand.
Argentina continue their World Cup campaign against Austria on Monday at 18:00 BST.
