"This year's two Nobel Laureates in physics have used tools from physics to develop methods that are the foundation of today's powerful machine learning," the Nobel committee said in a statement.
US scientist Hopfield's research is carried out at Princeton University and Hinton, a British-Canadian, works at the University of Toronto.
Ellen Moons, a member of the Nobel committee at the Royal Swedish Academy of Sciences, said the two laureates "used fundamental concepts from statistical physics to design artificial neural networks that function as associative memories and find patterns in large data sets".
She said such networks had been used to advance research in physics and "have also become part of our daily lives, for instance in facial recognition and language translation".
While the committee honored the science behind machine learning and artificial intelligence, Moons also mentioned its flip side, saying "while machine learning has enormous benefits, its rapid development has also raised concerns about our future".
"Collectively, humans carry the responsibility for using this new technology in a safe and ethical way for the greatest benefit of humankind."
Hinton shares those concerns. He quit a role at Google so he could more freely speak about the dangers of the technology he helped create.
On Tuesday, he said he was shocked at the honour.
"I'm flabbergasted. I had, no idea this would happen," he said when reached by the Nobel committee on the phone.
Hinton said he continues to worry "about a number of possible bad consequences'' of his machine learning work, "particularly the threat of these things getting out of control", but still would do it all over again.
Six days of Nobel announcements opened on Monday with Americans Victor Ambros and Gary Ruvkun winning the medicine prize for their discovery of tiny bits of genetic material that serve as on and off switches inside cells that help control what the cells do and when they do it.
If scientists can better understand how they work and how to manipulate them, it could one day lead to powerful treatments for diseases such as cancer.
The physics prize carries a cash award of 11 million Swedish kronor ($A1.6 million) from a bequest left by the award's creator, Swedish inventor Alfred Nobel.
The laureates are invited to receive their awards at ceremonies on December 10, the anniversary of Nobel's death.
Nobel announcements continue with the chemistry physics prize on Wednesday and literature on Thursday.
The Nobel Peace Prize will be announced on Friday and the economics award on October 14.
