The work depicts Jobs in his trademark black turtleneck jumper carrying an early model of his Apple computer and with a black bin bag slung over his shoulder.
The portrait by the elusive street artist has appeared on a graffiti-littered concrete wall on the outskirts of The Jungle camp where 6,000 migrants from countries including Syria, Afghanistan and Eritrea are based.
The piece has gained such popularity in the area, close to the Port of Calais, that migrants have covered it up with a blanket and are charging people to view it.
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One migrant who emerged from a tent beside the concealed artwork said: "If you haven't got five euros (£3.60) then go away."
The father of Jobs, who died in California in 2011 aged 56 after suffering pancreatic cancer, was from the Syrian city of Homs but emigrated to the US.
In a rare statement to accompany the work, Banksy said: "We're often led to believe migration is a drain on the country's resources but Steve Jobs was the son of a Syrian migrant.
"Apple is the world's most profitable company, it pays over 7 billion dollars (£4.6 billion) a year in taxes - and it only exists because they allowed in a young man from Homs."
Authorities in Calais are reportedly planning to shield the life-size portrait, along with two other Banksy works in the northern French port city, the Press Association reported.
Calais mayor Natacha Bouchart told local newspaper Nord Littoral that the artwork had a "positive message" and was an opportunity for the city.
In the summer, Banksy's temporary theme park at a derelict lido in Weston-super-Mare, Somerset, featured migrant boats in water filled with bodies.
Dismaland, which sold out every day of its five-week run, also included Jimmy Savile, an anarchist training camp and a fire-ravaged Cinderella castle.
After the park closed, the timber and fixtures from the site were transported to Calais to build shelters for people who had fled conflict, persecution and poverty.