Barouch faces a charge of possession of an unregistered destructive device.
The device, discovered Sunday outside the Colleyville woman's home, did not detonate. An affidavit said the box had two salad bowls taped together, a battery and powder.
Prosecutor Bret Helmer said Barouch failed to move on after the divorce and thought it would be better to put a bomb on his ex-spouse's porch.
Barouch was arrested Wednesday after alleged bomb-making materials were confiscated at his home. Agents said they found a will and last testament that was dated May 2 -- the same day his former wife found the bomb on her front porch -- during a search of his north Fort Worth home.
He went before a federal magistrate Thursday.
Defense attorney Matthew Belcher said there is good evidence that Barouch should be released.