The migrants rescued on Friday told police another 23 people had been aboard before the boat began to sink. Police managed to rescue one man from the water but there was no immediate sign of the other 22.
Lopez said the search was continuing Friday morning.
The missing include 19 men, one woman and two children. Amond the survivors were 23 men, two women and one child. Two were being treated in a Motril hospital for hypothermia while the rest were being cared for by the Spanish Red Cross.
Lopez said they do not yet known where the boat came from. Each year thousands of migrants from Africa try to reach Europe by setting sail in small, fragile boats. Dozens are believed to drown while attempting the dangerous journey.
A European Union surveillance system called Frontex tries to detect incoming migrant boats and intercept them before they reach the mainland or offshore outposts such as Spain's Canary Islands.
The number of migrants arriving in Spain has dropped considerably since it reached a peak of 32,000 in 2006.