The 33-year-old, from Reservoir in Melbourne's north, was charged on Thursday with four counts of using a carriage service to menace, harass or cause offence and one count of using a carriage service to threaten to kill.
Both charges carry a maximum penalty of five years' imprisonment.
The man allegedly used social media to make death threats and anti-Semitic comments to the NSW-based Federal MP several times between January 16-18.
He is also accused of using social media to contact a Victorian-based state MP in the same month.
A search warrant was executed by Australian Federal Police and Victoria Police at the man's home on Thursday and several electronic devices were seized.Â
AFP Counter Terrorism and Special Investigations Command Assistant Commissioner Stephen Nutt said the charges should be a warning for anyone considering similar conduct.
"Anyone engaging in this type of deplorable behaviour will be investigated, located and brought before the court," he said.
"Parliamentarians and members of our community should not have to endure vile threats based on their race, religion, or ethnicity.
Mr Nutt anticipates further charges to be laid given the experienced team working on Special Operation Avalite has a number of individuals under investigation
Mr Albanese pleaded for the heat and polarisation which has taken hold in some democracies overseas to be turned down in controversial issues, revealing the security of parliamentarians, including himself, were constantly monitored.
"The truth is that we do live in circumstances where the number of threats that have been made towards elected representatives (has increased)," he told reporters on Friday.
"People will say things on social media that they would never say to you face to face, and they engage in a way that seems to ramp up from zero to 11 straight away to be able to have civil discourse in this country.
"I don't want to see the sort of polarisation that we see in some of our democracies around the world happen here."
The man was granted conditional bail and is scheduled to appear before Melbourne Magistrates Court on April 8.