A man is on the run after allegedly stabbing his cousin in one Melbourne suburb before driving across the city to attack his sister.

The man, aged in his 20s, is alleged to have forced his way into a Bradman Trc sharehouse in Epping before stabbing a 40-year-old man – believed to be his cousin – about 7.30am on Sunday.

He was taken to hospital with non life threatening injuries.

The man is then believed to have made his way across town to a home in Dandenong North, allegedly crashing his silver Honda CRV, which is believed to have been stolen, into the house about 10.15am.

The man allegedly went inside the house and stabbed a 34-year-old woman – believed to be his sister – multiple times.

She was taken to hospital in a serious condition.

Both victims sustained multiple upper body injuries, with police believing both events were targeted.

“We’re not taking any risks… we don’t know if he still has a weapon on him,” Inspector Graham Higginbotham said.

Higginbotham said the police helicopters and dog squads were joining the search for the man, with multiple police patrols continuing searches of local areas.

The man is described as African in appearance with “afro-type” hair, and wearing a dark-coloured track suit.

“There’s a fully active and ongoing investigation to try and locate this person,” Higginbotham said.

“This appears to be instances against persons known to this person, so we’re not saying there’s potential for random attacks out there, but we just ask people to be careful and cautious and to contact police if they do see anyone matching that description.”

He said police do not believe there’s a risk to the larger community, however, local residents said it has left them shaken.

“I feel really scared,” one person told 7NEWS.

Another woman said she and her husband saw the alleged offender calmly walk down the street after the attack.

“(He) was so blase,” she said.

“He just walked down the street and then he just disappeared.”

Police have urged anyone with CCTV footage or information as to the mans location to contact police.

Members of the public have also been advised not to approach the man but to call triple-0 if they sight him.