Mr Morrison said Australia would implement a "rolling wave" of sanctions to put further pressure on Russia.
The decision came amid reports of at least 100 Ukrainian deaths in fighting and the capture of the disused Cherynobyl nuclear power plant.
Ukraine's foreign minister Dmytro Kuleba described Russian rocket strikes on the capital Kyiv as "horrific" and called on world leaders via Twitter to "kick Russia out of everywhere".
The new Australian sanctions, which will mirror similar moves from the US and UK, will apply to 300 members of Russia's parliament who voted to authorise the military action, as well as Russian oligarchs of "strategic significance".
The prime minister said Australia would work with American authorities to align sanctions against Belarusians who were complicit with Russian acts of aggression.
"Russia has been planning these acts of violence for some considerable period of time, but there must be a cost, there must be a price and it must be imposed by the global community," Mr Morrison told reporters in Adelaide.
"We understand the concern that the threat of sanctions did not lead to (Russia) not going ahead with this. That was not our expectation."
Australia will also work alongside NATO partners to provide non-lethal military equipment and medical supplies to Ukraine.
"We are providing financial support as well as equipment through that NATO channel," Mr Morrison said.
The prime minister singled out China for failing to call out the Russian invasion of Ukraine and impose sanctions.
Mr Morrison said it was concerning China was easing trade restrictions with Russia.
"This is of great concern to Australia that these acts are not being called out with the same voice when it comes to those in our region."
Mr Morrison and Finance Minister Simon Birmingham met with members of the Ukrainian community in Adelaide, as hundreds of people rallied around the country urging the government to provide more support.
Foreign Minister Marise Payne said Australia was working closely with other nations to apply pressure on Russia.
"There are no alternatives to sanctions, the alternative is no penalties and no costs and that is unacceptable," she told Sky News.
"(Russian President Vladimir Putin) clearly wants to reverse history and force Ukraine back under authoritarian control, but Ukraine has chosen a different path and a path of democracy."
Previous rounds have included sanctions on Russian army commanders, mercenaries responsible for attacks and eight members of Russia's security council.
Multiple Russian financial institutions have also been targeted.
Opposition Leader Anthony Albanese also urged countries like China to act against Russian aggression.
"China is doing the exact opposite (of sanctions) by lifting restrictions on wheat trade, it is doing the opposite of what it should be doing," Mr Albanese told reporters in Tasmania.
Mr Albanese said it was critical for all countries to condemn Russia for its act of aggression in Ukraine.
"It's important that the entire world act against this aggression and say that it is completely unacceptable. And to do that, we need punitive action against Russia."
Defence Minister Peter Dutton said Mr Putin had retreated to a Cold War era mentality.
"(Mr Putin) believes that Ukraine's territory should be part of Russia and that's his intent. He's 69 years of age and he wants to see it in his lifetime," he told the Nine Network.
"We should be very careful about autocrats like this who have this worldview that they want to go back to a Cold War era or back to a period of conflict and that's a price that they're willing to pay."