Allan Rubin said she died on Sunday of natural causes, AP reported. She was living in Princeton, New Jersey.
Her studies earned her numerous honours, including being the second female astronomer to be elected to the US National Academy of Sciences.
But many questioned why she was never awarded a Nobel Prize.
In 1974, Rubin discovered that the stars at the edges of galaxies moved faster than expected.
Gravity calculations using only visible matter in galaxies showed that the outer stars should have been moving more slowly.
To reconcile her observations with the law of gravity, scientists proposed there was matter we cannot see and called it dark matter.
Dark matter is an unidentified type of matter comprising approximately 27% of the mass and energy in the observable universe.
Vera Rubin's interest in astronomy began as a young girl and grew with the involvement of her father, who helped her build a telescope and took her to meetings of amateur astronomers, according to a profile of the American Museum of Natural History.
She was the only astronomy major to graduate from the prestigious women's college Vassar in 1948. When she sought to enrol as a graduate student at Princeton, she was told that women were not allowed in the university's graduate astronomy programme, a policy that was not abandoned until 1975.
So she applied to Cornell University, where she studied physics. She then went on to Georgetown University, where she earned her doctorate in 1954.
Later she moved on to work at the Carnegie Institute of Washington. In 1993 she was awarded the US National Medal of Science.
Astronomer Vera Rubin, whose pioneering work on galaxy rotation rates led to the theory of dark matter, has died at the age of 88, her son says.