The Swiss citizen was in hospital in Zurich and died on Saturday, the statement by the Public Prosecutor's Office of the Canton of Valais added, without providing any further information.
Most of those killed in the blaze at Le Constellation bar were teenagers and some of the 116 people who were injured are still in hospital with severe burns.
The additional victim was a young man living near the western city of Lausanne, two sources with knowledge of the matter told Reuters.
On Saturday, hundreds of people marched alongside bereaved parents through the lakeside town of Lutry near Lausanne, carrying a large banner demanding "truth and justice".
"Today, we are just asking for justice and truth and afterwards we will mourn," Laetitia Brodard-Sitre, who lost her 17-year-old son Arthur in the fire, told a crowd of people carrying white roses.
The fire has tested relations with neighbouring Italy, which lost citizens in the blaze and has protested the release on bail of the bar's owner.
Swiss authorities earlier this week said they would grant the Rome Public Prosecutor's Office access to evidence gathered.
The prosecutor said in a statement on Sunday it would provide no further information on the status of the investigation.
with AP
