There have been more than 60 attempts on the seven-metre (23-foot) high fence around the tiny Spanish outpost this year, mostly at night, according to officials.
"Around 16 migrants tried to get over the fence in the northern zone and 10 succeeded," a spokeswoman for Melilla's prefect said, before they were taken to a immigration centre.
Around 500 migrants, organised into small groups, tried to approach the heavily-guarded frontier on Thursday but were pushed back by Moroccan police.
As many as 15,000 migrants have tried to get into the Spanish enclave since the beginning of the year, with 2,000 succeeding, officials said.
The two Spanish-governed enclaves of Ceuta and Melilla are Europe's only land borders with Africa.