Speaking in a parliamentary commission on internal affairs, he added that the number of people merely attempting to get to the Spanish overseas territory of Ceuta in northern Morocco had dramatically increased.
Up until Monday, 15,473 migrants had entered Spain illegally by sea and over land, he said.
Of the 11,162 people who arrived by sea, some 11,000 were rescued by coastguards from rickety boats in which they were crossing the Mediterranean between Morocco and Spain.
The others arrived on their own.
At least 121 people have died along the way, according to the International Organization for Migration (IOM).
Many Africans undertaking the long route to Europe are choosing to avoid crossing danger-ridden Libya to get to Italy along the so-called central Mediterranean route, and choosing instead to get there via Morocco and Spain.
But figures show that the route to Italy is still the most popular, with some 100,000 people arriving so far this year.
Zoido said there had been a leap in coordinated attempts to break through high double border fences or storm frontier posts in Ceuta, which with Melilla, another Spanish territory in northern Morocco, represents the only land border between Africa and Europe.
He said that so far this year, close to 9,000 people — mostly from sub-Saharan Africa — had attempted to force their way into the Spanish territory compared to 613 in the same period in 2016.
“There is a constant trickle of people attempting to break through Ceuta's fence,” he said.
He added that the double fence in Ceuta, built in 1999 and increased in height from three to six metres (10 to 20 feet) in 2005, “doesn't fulfil the purpose for which it was once built.”
“The migrants use tools such as clubs, metal cutters or hooks to break doors in the border fence and cut or climb over the fences,” he said.
The Spanish government aims to invest some €12 million ($14.4 million) next year to shore up the border fence between Morocco and Ceuta, by for instance reinforcing security along the barrier.