Twenty-two-year-old Jessica Tata has returned to her home in Nigeria just four days after the tragedy on Crest Park at Waypark in west Houston.
Fire Department Assistant Chief Michelle McLeod refused to reveal how she knew Tata had gone on the run.
But passport coding has verified she took a flight out of Dallas, possibly as early as Saturday afternoon.
The U.S. Marshals Service in Houston has been asked to help track her down, said spokesman Alfredo Perez.
He added: 'Just because someone who is wanted flees to another country doesn't mean the United States isn't going to get them back and have them face justice.
'We’re looking for her. We’re actively working this case as a fugitive investigation.'
Perez confirmed that if Tata is in Nigeria, the U.S. will ask the country to arrest her.
Tata, owner of Jackie's Child Care, was charged with reckless injury to a child involving serious bodily injury. If convicted, she faces a sentence of two to 10 years in prison.
A warrant was issued for her arrest on Sunday by the Harris County District Attorney's Office and the bail bond was set at $500,000.
Neighbours claim Tata had gone to a store and arrived at the centre - her one-storey private home - in her minivan with grocery bags.
They told investigators they heard her screaming seconds after she went in the front door and saw smoke coming from inside.
'Both witnesses said they saw no adults or employees of the day care either inside the building or running out other than (Tata),' said the affidavit.
'This is the first time I am even hearing about it. So I'm just hoping she turns herself in.'
Firefighters arriving at the scene last Thursday lunchtime found two injured children outside the home and five more trapped inside.
Three of the children, including Elizabeth Kojah, of Cypress, and Kendyll Stradford, of Katy, both 20-months-old and Shomari Dickerson, aged three, died on Thursday.
A fourth child, Elias Castillo, died on Saturday.
Emmanuel Kojah, who lost his daughter said he forgives Tata.
He said: 'You could feel angry, bitter, anything ... you could kill her ... but to what effect ... those kids are already gone.'
Mr Kojah said he fed his daughter mango and changed her diaper Thursday morning before she went to day care.
He said: 'She hugged me really tightly. She was a beautiful child.'