The speed of the bill's approval has raised suspicion among Kremlin critics.
Some political analysts say that the constitutional reform could be used as a justification for holding an early presidential election in which Putin, who remains popular in the country, could run again.
The bill now has to be approved by two-thirds of Russia's regional legislatures in what is seen as a foregone conclusion.
It must then be voted on by the federation council a second time and signed into law by Medvedev.
The bill's supporters say the approval process will take about a month. If passed, the amendments would be the first changes to Russia's post-Soviet constitution since its adoption under Boris Yeltsin, the former president, in 1993.
"I expect we can look at the decisions of the subjects of the Russian federation on the laws adopted today... at a hearing on December 22 or December 30," Sergei Mironov, the federation council speaker said.
The constitutional amendments include an extension of parliamentary terms from the current four years to five as well as a provision for the government to report to parliament on a regular basis.
Medvedev said the reforms were needed to increase political stability.
In a commentary on Wednesday, the Nezavisimaya Gazeta daily newspaper said that Russian authorities could be pushing the changes through so that they are in place ahead of celebrations to mark the 15th anniversary of the Russian constitution on December 12.