Milner, who set up his prize this year to address what he regards as a lack of recognition in the modern world for leading scientists.
Alongside Hawking, a second $3 million award has gone to the scientists behind the discovery this year of a new subatomic particle that behaves like the theoretical Higgs boson, imagined almost half a century ago and responsible for bestowing mass on other fundamental particles.
The scale of the awards from the Milner foundation - and being able to give them to multiple recipients for huge projects - could, over time, see them compete in prestige terms with the annual Nobel prizes.
The Nobel committee has had to scale back the size of its awards in line with the performance of the investments which support it. Each prize is now worth $1.2 million, down from about $1.5 million in recent years.
Diagnosed with motor neurone disease at the age of 21 and told in 1963 he had two years to live, Hawking, now 70, has become one of the world's most recognisable scientists after guest appearances on The Simpsons and on Star Trek.
At the opening ceremony of the Paralympic Games in London in August, speaking through his computerised voice system, he said: "Look up at the stars and not down at your feet. Be curious."
He was awarded the Special Fundamental Physics prize for what the committee called his "deep contributions to quantum gravity and quantum aspects of the early universe" as well has his discovery that black holes emit radiation.
"No one undertakes research in physics with the intention of winning a prize. It is the joy of discovering something no one knew before," Hawking said in comments emailed to Reuters.
"Nevertheless prizes like these prizes play an important role in giving public recognition for achievement in physics."
Hawking said he planned to use the money to help his daughter with her autistic son and may buy a holiday home.
He shares the limelight with leaders of the project to build and run the Large Hadron Collider (LHC) particle accelerator at the CERN research centre near Geneva, which led to the discovery of the particle that is thought to be the boson imagined by theorist Peter Higgs in 1964.
In the Standard Model, which governs scientific understanding of the basic make-up of the universe, the Higgs boson gives mass to other fundamental particles.
But in the half century before scientists at CERN started smashing particles together in the LHC and studying the results, it sat in the realm of theory.
Although the work of building the LHC and running experiments in the particle accelerator involved thousands of scientists and engineers, the prize has been awarded to past and present team leaders.
The winners include the head of the LHC Lyn Evans, and the two spokespeople, Fabiola Gianotti and Joe Incandela, who presented the discovery to applause and cheers from the gathered physicists at CERN earlier this year.
Michel Della Negra, another prize-winner who for 15 years from 1990 led a team that built one of the two giant detectors used to find the Higgs, said the award was a big surprise.
"I didn't even know the prize existed," he told Reuters.
Della Negra receives $250,000 because the $3 million is to be split three ways between Evans, and the two teams working on the Atlas and CMS detectors. Two leaders of the Atlas team will get $500,000 each while the four from CMS get $250,000 apiece.
Gianotti and Incandela both plan to put their prize money back into science.
"We have 3,000 people from 38 countries in the Atlas collaboration, so the money will be used for helping young scientists who need financial support," Gianotti said.
Because the Nobel rules allow a maximum of three people to share one prize, some scientists argue they are out of touch with the large-scale collaborations that are a feature of much modern research.
Milner's new prize is more flexible, significantly more lucrative.
"I'm really impressed," said Incandela. "They are trying to modernise the way prizes are done."