The French centre-back has a fresh knee problem, the Catalan club revealed in a statement last Friday, and was expected to be out until at least the end of LaLiga.
Umtiti is undergoing conservative treatment and, asked about the World Cup winner's fitness on Friday, Setien said: "He is in an acute process with his problem."
And he admitted: "Not even the doctors know how long he will be out."
The 26-year-old has been plagued by knee problems since an excellent debut season at Camp Nou in 2017-18, having forced himself through the pain barrier – by his own admission – to take part in the World Cup in Russia.
He has not featured since playing the 90 minutes in the 2-2 draw at Celta Vigo last month and will be made available for transfeer this summer, although his injury problems could make an exit difficult.