Police Inspector Glenn Weir said on Monday the shooting appeared to stem from a domestic incident between the gunman and the woman.
"It does appear that there was a relationship between the female and the male suspect and certainly we're not looking that it's a random act, certainly not gang-related… it appears as though it's a domestic-related incident," Weir said.
Police believe Hudson may have fled the city in a black Mercedes sedan or a black SUV after the shooting.
Victoria police detective Inspector Stephen Clark said on Tuesday that arresting Hudson "is our number one priority".
Clark said the third wounded person was a Dutch backpacker, whose family was flying to Australia, on an extended holiday.
Local media reported that Hudson was a Hell's Angels member with a record of violence and gang rivalry previously.
Monday's shooting threw Melbourne central business district into chaos during the morning rush hour with commuters fleeing in panic.
Several blocks of the city centre were sealed off and evacuated as elite police hunted for the gunman.
Police later found s handgun and a dark jacket at a nearby construction site.
Zali Nash, an eyewitness, told ABC radio the gunman was "as cool as a cucumber" as he shot the victims.
"There were five shots fired and the people went straight down to the ground. There wasn't even a scream, just a whimper"
Zali Nash, eyewitness
"He just went bang, bang, bang, there was no mucking around," she said. "There were five shots fired and the people went straight down to the ground. There wasn't even a scream, just a whimper."
Melbourne has in recent years experienced a bloody gang war which began in the late 1990s.
Police suspect the upsurge of violence between motorcycle gangs is linked to the illicit drug trade.
One of the worst public shootings in Melbourne occurred in 1987 when seven people were killed and more than a dozen were injured in a shooting spree by a former army cadet.