The arrest was made at 11.20am in the suburb of Greensborough, close to Bundoora where her body was found.
"Homicide Squad detectives have arrested a man as part of the ongoing investigation into the death of Aiia Maasarwe," Victoria Police said in a statement.
"The arrest followings an extensive investigation into Aiia’s death following the discovery of her body near Main Drive and Plenty Road in Bundoora on Wednesday 16 January about 7am."
Sergeant Julie-Anne Newman thanked the public for their help in the investigation.
It is believed the man will be questioned by police over coming hours.
Police believe she was set upon after she alighted from a number 86 tram on Plenty Rd and began walking near Main Drive.
She had been returning home from a comedy show on Wednesday.
Tonight, hundreds of people draped in black will sit silently on the Victorian parliament steps before packing the 86 tram full of flowers and candles - a moving tribute to 21-year-old.
Tributes have popped up on social media, offering places for Melbourne residents to come together and reflect on the latest horrific event to plague the city.
'Keeping Silent Vigil' is inviting people to gather on the steps of Parliament at 6pm to "honour the lives of women and children so brutally ended by male violence".
Co-organiser Jessamy Gleeson, who was also involved in organising the vigil for Eurydice Dixon last year, said she was "shattered and heartbroken" to be organising another event just six months later.
More to come
