, 31, drove a 20-ton truck through hundreds gathered to watch the Bastille Day fireworks Thursday night on the Mediterranean city's waterfront.
Agnes Thibault Lecuivre, a spokeswoman for the anti-terrorism prosecutor, did not provide details on the couple's connection to the terror attack.
French authorities said six people are in custody in connection with the attacks. Bouhlel's estranged wife was arrested at her apartment Friday and released Sunday morning without charge, her attorney, Jean-Yves Garino, told CNN. Garino said the woman, the mother of Bouhlel's three children, had not been in contact with the attacker since they were in the middle of divorce proceedings.
Bouhlel was shot to death by police after he barreled down the crowded Promenade des Anglais for almost a mile, crushing and hitting people who had gathered to watch fireworks. More than 200 people were injured.
Authorities identified him by fingerprints after his identification card was found in the truck.
ISIS: 'Soldier' behind attack
ISIS' media group, Amaq Agency, said Saturday that an ISIS "soldier" carried out the attack.
In a statement, it said "the person ... carried out the operation in response to calls to target nationals of the coalition which is fighting the Islamic State."
Bouhlel hadn't shown up on any anti-terrorist intelligence radar, French Interior Minister Bernard Cazeneuve said.
He had no record of making militant statements and was not known to the intelligence services, the minister said.
"It seems he became radicalized very quickly," Cazeneuve said Saturday, without offering specifics.
Bouhlel, a resident of Nice, was born in Tunisia but had a permit to live and work in France.
He was known to police because of allegations of threats, violence and thefts over the past six years, and he was given a suspended six-month prison sentence this year after being convicted of violence with a weapon, authorities said.
Despite his criminal record, he was not on the radar for any kind of terror threat. The man was "entirely unknown by the intelligence services, whether nationally or locally," French prosecutor François Molins said.
"He had never been the subject of any kind of file or indication of radicalization."
Before the attack
The attacker sent a photo of himself from among the crowds celebrating Bastille Day shortly before he rammed his truck into them, his brother Jaber Bouhlel told CNN Arabic from his hometown of Msaken, Tunisia.
Mohamed Bouhlel seemed "so happy and there was no sign that he was planning for something bad," his brother said.
The family is not releasing the photo to the media.
Bouhlel's father said his son showed signs of mental health issues -- having had multiple nervous breakdowns and exhibiting volatile behavior, said CNN terrorism analyst Paul Cruickshank.
Threat to France
Cruickshank said "no country in the Western world is threatened more by jihadis and terrorism than France."
"This is a big step back here. They are absolutely exhausted after a year and a half of intense efforts to try and protect this country," he said.
"The painful reality here is that if it wasn't going to be this promenade, it would have been any other promenade."
France had put intense security in place for Euro 2016
, the international soccer tournament that just ended. No major attacks occurred during the event.
About 85 people are still hospitalized in the wake of Thursday's attack, with 29 patients in intensive care, said Marisol Touraine, French minister of social affairs and health.
Touraine said 18 patients remain "between life and death," including one child.
Around 500 people in Nice have sought psychological support in the aftermath of the attack, she said.
Meanwhile, Nicolas Leslie, a University of California, Berkeley, student who had been missing after the attacks, is confirmed dead, the school said Sunday, relaying information it had received from the FBI. He is the third American confirmed killed in the Thursday attack. A father and son from Texas also died in the attack.