According to Spain's Europa Press news agency, the incident occurred at 7:20 a.m. local time (05:20 GMT) near the breakwater of the town of Benzu, where the 8.2-kilometer (5.09-mile) border fence ends.
Five Civil Guard servicemen received minor injuries, but some of the migrants were more gravely injured.
The Spanish enclaves of Melilla and Ceuta in northern Africa, which are separated from mainland Spain by the Strait of Gibraltar, are popular transit points for sub-Saharan African migrants aiming to get asylum in the European Union.