She said that Spanish rescue boats, aeroplanes, divers and helicopters from three ports had rescued 11 people - seven men and four women - but gave no further word on their condition.
Moroccan security services said between five and seven people had died, while 20 to 30 people had survived.
A civil guard helicopter noticed the sinking boat just after 9am (0700GMT) off the disputed island known as Perejil to Spaniards and Leila to Moroccans, in Moroccan waters near Ceuta, and the Royal Moroccan Navy was alerted.
Dozens of boats leave Africa ferrying migrants who hope to reach Europe every year.
A primary target location is the Canary Islands in the Atlantic Ocean, a Spanish territory.
Authorities fear that thousands of people die annually taking the journey, due to thirst, hunger or sun exposure, although it is impossible to know exact figures.