The man slashed the throats and faces of people in Rackhams before being overpowered by two unarmed police officers after a struggle.
Last night a 30-year-old Birmingham man was being questioned by West Midlands police over the incident.
The wounded were taken to Birmingham General Hospital; three women required stitching under general anaesthetic; and, two of them will need plastic surgery.
Nine of the victims worked at Rackhams, including two security guards, and six were customers. Five other people were treated for shock.
Dr Victoria Vella, from the casualty department said: ''Most of them sustained cuts around the neck and face. It was fortunate that all the slash wounds missed the main artery in the neck.''
The attack began in the perfume department when the man called over an employee and stabbed her in the neck. Armed with a 12-inch serrated bread knife and a long meat boning knife, he then rampaged through two floors of the store for 10 minutes.
Clare Dallaway, who was promoting the National Lottery, said: ''It was awful. This man was just slashing at women's throats with a knife.''
Another witness, Tony Parker, saw the man holding a shop assistant around the throat. ''It looked as though her throat had been cut. The man then grabbed another woman and cut her as well.
''Next to the two who had been stabbed, I saw another elderly woman who also had her throat cut. She was obviously in deep shock because she seemed very calm. I helped her to the ground floor and tried to stop the bleeding to her neck.''