Victorian health authorities say there is a low likelihood the man is infected, because he had not disembarked when the ship docked in China and it had been 14 days before symptoms developed.
Test results are expected later on Monday.
A rescue boat arrived at Port of Hastings shortly before 7.13pm on Monday, maritime records show.
Maritime logs show an LPG tanker named The Promise docked there on Monday afternoon, after leaving Zhoushan in China on January 26.
The department spokesman could not confirm whether The Promise was the ship in question.
Zhoushan is part of the Zhejiang province in eastern China. The Promise is expected to set off for Shanghai on Friday.
Australia has 15 confirmed cases of coronavirus, four in Victoria, four in NSW, five in Queensland and two in South Australia.
“All of the cases in Australia have come from Wuhan except one in NSW who had contact in China with a confirmed case in Wuhan,” the federal Department of Health said.
“Of the previously reported cases, five have recovered. The others are in a stable condition.”