Police in Melbourne are appealing for witnesses after a basketball exploded on a beach at Black Rock, leaving a woman with serious burns.

The woman, 21, from Kerang, in northern Victoria, was walking along the beach at Half Moon Bay around 10:30pm on March 17 when she saw a basketball in the sand.

"As she went to pick it up, it exploded, leaving her with burns to her face, head and forearms," a police statement said.

"She then rushed to the water to try and cool down and was later transported to hospital by paramedics."

Police were told that a group of men may have rolled the ball towards the woman and then walked away, but police were not sure if the men intended for anyone to pick up the ball.

"At this time the reason for the explosion is unknown and police are not sure whether the group had intended for anyone to pick up the ball or why the group had it at the beach.

"It's believed the ball may have had sparklers or similar attached to it."