Medvedev said the proposals would make significant changes to the country's balance of power and so "the government in its current form has resigned."
Medvedev made the surprise announcement on Russia's state TV while sitting next to Putin who thanked him for his work.
The Russian prime minister submitted his resignation to President Putin, reports said. "All further decisions will be taken by the president," Medvedev stated.
Putin named Mikhail Mishustin, Russia's head of tax service as a replacement for Medvedev.
In a speech, the Russian president had said, "It was necessary to conduct a vote by the country's citizens on an entire package of proposed amendments to the country's constitution."
Putin, 67, is set to step down as president in 2024 with Russia set for parliamentary elections in 2021. Under the Russian constitution, a person cannot serve more than two successive presidential terms.
In December, during a marathon press conference, the Russian president had dropped broad hints that he might not seek another term in 2024.