Pensioners are to receive 10,000 roubles ($A241) per month and women are to receive a one-off payment of 20,000 roubles ($A481) for the birth of a child.
Refugees forced to leave their homes because of the war are eligible, according to the decree that was published on Saturday.
Millions of people are fleeing, either displaced within Ukraine or trying to escape to other countries from Europe to Russia, due to the war launched by Moscow on Ukraine in February.
Some 3.2 million refugees had reached Russia by the beginning of August, according to the Russian authorities, although it was not possible to verify the figure.
The Ukrainian government has repeatedly accused Moscow of deporting people and keeping them in special camps.
Human rights activists have pointed out that some Ukrainians have been forced to leave their country for Russia during evacuations or via safe corridors, for example.
Other Ukrainians have left their country to live with relatives in Russia.
Meanwhile in Russia, Ukrainians who have fled the war have set up a range of private initiatives to help others who are following in their wake.