His daughter broke the news of the death of Rubinstein, a prominent opponent of Russian President Vladimir Putin.
"My father, Lev Rubinstein, died today," his daughter Maria wrote on her blog.
Rubinstein, 76, was hit by a car on January 8 and was in a coma for six days.
Rubenstein was known as one of the founders of the conceptualist art movement.
This movement, prominent in the Soviet Union in the 1970s and 1980s, used art in many forms to criticize the official doctrine of socialist realism and subvert traditional Soviet-era norms.
The movement represented an approach in which artworks were based primarily on an intellectual concept and visual form was secondary.
"With his shocking poetry, wit and irony, he was the epitome of the way the world was perceived," Memorial human rights organization said of Rubinstein in a condolence message after his death.
Memorial, one of the oldest civic groups in Russia, was shut down in December 2021 over its opposition to Russia's war in Ukraine.
Rubinstein, whom Memorial described as a close friend, also took a strong stance against Russia's invasion of Ukraine and the Russian government's treatment of LGBT rights.
Rubinstein has remained in Moscow for two years "against all odds," the group said.
Rubinstein rose to widespread fame after the collapse of the Soviet Union. His writing was published by mainstream publishing houses.
The Moscow Transportation Department said the car that hit Rubinstein while crossing the street "did not slow down."
The department said that according to preliminary information, the driver who hit Rubinstein had committed 19 traffic violations in 12 months.
Authorities said they have launched an investigation into the accident.