The ministry has asked Russia's supreme court to close the group's headquarters and stop its 175,000 Russian members sharing "extremist" literature.
A spokesman for the group called the proposed ban "persecuting worshippers just for manifesting their faith".
Some Russian regions have already shut down branches of Jehovah's Witnesses.
According to the justice ministry, the Jehovah's Witnesses' activities "violate Russia's law on combating extremism".
The authorities object to pamphlets deemed to incite hatred against other religious groups, mainly for proclaiming Jehovah's Witnesses as followers of the only "true" faith.
One quotes the novelist Leo Tolstoy, describing the doctrine of the Russian Orthodox Church as superstition and sorcery, the BBC's Sarah Rainsford reports from Moscow.
The group was registered in Russia in 1991.
Thousands of Jehovah's Witnesses were deported to Siberia during Joseph Stalin's 30-year reign of terror. Other Christian groups were also persecuted at the time.
Russia's justice ministry has called for a ban on the Jehovah's Witnesses, a Christian movement that zealously seeks converts and rejects military service.