Jacques Moretti and his wife Jessica are under investigation for negligent homicide and other crimes linked to the blaze that killed 40 people and injured more than 100, many of them teenagers.
Many of the survivors are still in hospitals across Europe with severe burns.
Jacques Moretti was detained on January 9. His bail arrangements include a 200,000 Swiss franc ($A367,500) payment and an order to report daily to a police station, the court said.
Italian Prime Minister Giorgia Meloni called the decision to release him "an affront to the memory of the victims of the New Year's Eve tragedy and an insult to their families, who are suffering from the loss of their loved ones".
"The Italian government will demand answers from the Swiss authorities about what happened," she wrote on X.
Six of the dead were Italian, as were 10 of those injured.
Lawyers for the victims and their families also said they were struggling to understand the court order and said their clients were concerned about evidence disappearing.
"My clients note that once again no consideration has been given to the risk of collusion or the disappearance of evidence - a risk that greatly worries them and jeopardises the integrity of the proceedings," said Romain Jordan, a Swiss lawyer for more than 20 families of victims.
The owners have both expressed grief over the tragedy and said they would co-operate with prosecutors.
"Jessica and Jacques Moretti will both continue to comply with all requests from the authorities," their lawyers said in a written statement after the release order.
Prosecutors said they had interviewed the bar owners about safety issues and renovations of Le Constellation bar during two hearings that had each lasted more than 10 hours.
They had also ordered searches, secured evidence and seized assets, they said.
