Victoria Police's Special Operations Group arrested the pair -- part of the Sudanese-dominated Apex street gang -- on Monday night, Xinhua news agency reported.
A police spokeswoman said in a statement on Tuesday: "It is believed the men are affiliated with the Apex gang, alleged to be involved in a recent spate of serious offences including aggravated burglary, car jackings and armed robberies."
On Saturday, almost 150 young men from rival gangs - Apex and Islander 23 - clashed in Melbourne's Federation Square in the midst of the family-friendly Moomba festival, sending bystanders fleeing in panic.
Police managed to disperse the crowd with batons and capsicum spray, but the rioters continued to rush through other parts of the city throwing metal chairs, among other objects, as they ran amok.
It is believed the gangs coordinated the gathering via social media.
Apex is a multicultural gang made up of youths of Sudanese, Pacific Islander, Maori, Afghani and Middle Eastern descent, while members of the Islander 23 gang predominately hail from the Pacific Islands.
Only four members of the two gangs were arrested on the night.
Since being founded in Melbourne's south-east 18 months ago, the Apex gang has marred multiple public events in Melbourne such as New Year's Eve and White Night and been linked to a rise in serious crime in the region.
A special police force, known as Taskforce Tense, was set up to crackdown on Apex members and has already made 33 arrests.