Feras Mousilli, 46, was arrested on Tuesday at Bush Airport and has since bonded out of jail.
Mousilli has been charged with sexual performance by a child.
A judge has issued a protective order, requiring he stay away from the 16-year-old and her family.
He has also been ordered not to use any smart phones or other electronic devices.
According to his firm's website, Mousilli specializes in technology law.
"There are electronic devices involved in this case that have evidence that's germane to this case. Essentially, it's pornographic evidence, and the concern for myself as the representative of the court at this point in time is I don't want you accessing any kind of child pornography or those kinds of things because this incident involves a child," a judge said.
Court documents show a 16-year-old girl reported to the Texas Department of Family and Protective Services that she had been having sexual intercourse and that she had met Mousilli on the dating app Bumble.
Investigators report finding screenshots and video on her phone, with at least one video from on or about May 10, according to those investigators, that showed both her and Mousilli naked.
"The evidence that I'm aware of is pretty damning. I'm not going to take the chance of you doing something else to some other kid if that's what happened. There is evidence of communication between you and the child that resulted in meetings where you allegedly did things with this child and, etc., so yeah, those are restrictions that I'm imposing," the judge told him.
Court documents show the girl told investigators she had shown Mousilli her passport with her date of birth and said he had admitted to her that he could go to jail.
Mousilli is due back in court in January.
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