Prosecutors are investigating the French owners on suspicion of crimes including homicide by negligence, while victims' families have filed legal complaints over the fire at the "Le Constellation" bar in Crans-Montana in the Canton of Valais.
Shortly after Swiss newspaper 24 Heures reported that one of the couple, Jacques Moretti, has been remanded in custody, prosecutors said they had issued an order for him to be held.
Under Swiss law, a person is held in custody until a court rules within 48 hours on whether their detention is warranted.
The Valais police declined to comment.
Early on Friday, Jacques and Jessica Moretti entered the prosecutors' office in the town of Sion for a hearing.
Hours later, video footage from Swiss broadcaster RTS showed Jessica Moretti leaving without her husband.
"My thoughts are constantly with the victims of this unimaginable tragedy that took place in our establishment and I would like to apologise to all the victims and those who are still struggling today," she said.
Swiss authorities have designated Friday a day of mourning and church bells rang out across the country for five minutes to honour victims.
The couple has said they would co-operate fully with the investigation.
More than half of those who died were teenagers and a further 116 people were injured, many of them seriously.
Several French and Italian citizens were among the dead, and Italy's Prime Minister Giorgia Meloni called for stern punishment to be meted out to those responsible for the blaze.
Italian President Sergio Mattarella and French President Emmanuel Macron joined Swiss leaders, victims' families and firefighters carrying white roses at a ceremony on Friday in the town of Martigny, where a minute's silence was held.
Dozens of people also stood near the shuttered bar in nearby Crans-Montana in silence, heads bowed under heavy snowfall.
Authorities placed hundreds of letters, teddy bears and bouquets of flowers for the fire victims beneath a protective igloo.
Speaking at the Martigny ceremony, Swiss President Guy Parmelin said he hoped that those responsible for the fire would be brought to account "without delay or leniency".
That must also include relevant political authorities, said Mathias Reynard, head of the Valais government.
Speaking in Rome on Friday, Meloni pledged to help the families of the Italian victims find justice.
"What happened in Crans-Montana is the result of too many people not doing their job or thinking they were making easy money. Those responsible must be identified and prosecuted."
Witnesses and prosecutors have said the blaze appeared to have been started by the use of sparkling candles that set foam soundproofing on the basement ceiling alight.
Questions remain about oversight at the bar, which the local mayor admitted this week had missed multiple safety checks.
Prosecutors said last weekend that the legal criteria to detain the bar's owners had so far not been met.
In a January 6 statement, the owners said: "We are devastated and overcome with grief, our thoughts are constantly with the victims, their loved ones who have been bereaved so brutally and prematurely, and all those who are fighting for their lives."
Twenty-one of the dead were from Switzerland, seven from France, and six from Italy.
A Swiss-French dual citizen and a French-British-Israeli citizen were also among the dead.
with DPA
