Daniel Buess, a drummer who performed with various electronic and “contemporary music” groups, was last seen at various restaurants in the city's red light district.
Police are now assuming that it is not a usual missing person's case and have opened up a criminal investigation.
“It's not normal that someone disappears as if swallowed up by the earth,” Peter Gill, a spokesman from the Basel prosecutor's office told 20 Minuten newspaper.
“We cannot exclude that something happened to him,” he said.
“We take this case very seriously.”
Friends of the musician have launched appeals on Facebook for anyone who may have seen him.
Basel police earlier issued a detailed description of the missing man.
He is about 180 centimetres tall, weighing around 65 to 70 kilograms, with a “lean physique” and a deep voice, police said.
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His long, light brown hair was tied up in a ponytail and he had stubble around his chin.
He has blue eyes and was wearing a piercing and earrings in his left ear lobe.
Buess has a tattoo of a serpent motif on his upper arm and was last seen wearing a black hooded jacket, black shirt and black pants.