"It is expected further inquiries in the coming days will determine the exact circumstances of what has taken place," police said.
"The boy's name is expected to be released later.
"Police would wish to offer their sympathy to the family of the boy at this tragic time.
"Police also want to remind all boat users out on the water this summer to take all necessary safety precautions before and on the water."
The matter has been referred to the coroner.
A St Bathans local, who did not want to be identified, said it was devastating.
"There were kids having a good time and then these boats came on. There shouldn't be any boats on the lake."
Blue Lake is a narrow, man-made 800m lake that was filled with water during extensive gold-mining operations in the area.
Now, it is a popular holiday spot for swimming, fishing and boating.
It has a Department of Conservation camp and this holiday season, with Central Otago enjoying high temperatures and long sunny days, has been extremely popular with families.
Yesterday was in the mid to high 20Cs and locals say the lake was busy with boats, kayaks, and swimmers.
"[A death] has been a possibility at that lake and a lot of people are aware of it ... it's a tragedy and it shouldn't have happened."
Many people have reacted to the tragedy by calling for a total boating ban on the lake.
"It was only a matter of time, it is by no means a lake for boating. Very sad," on the Facebook page of the Otago Daily Times.
"A dingy or two on the lake for a fish is all its [sic] really any good for. Family power boating and skiing, absolutely not."
Anette Becher said boats on Blue Lake have "massively increased in numbers" over the past 2-3 years.
She claimed there was up to four boats on the lake at any one time yesterday, including "a jet boat that recklessly went right across the edges where people were swimming".
Many others also used the forum to say the lake is far too small for motor boats.
While Dot Mulder expressed sympathy for the boy's family, she also felt for whoever was controlling the boat which struck him and who has to "live with this the rest of their lives too. Sad for everyone".
Meetings had been held with Otago Regional Council and rules governing boating on the lake were brought in about two years ago. This included a limit on the number of boats allowed on the lake at the same time, restricted boating hours, and speed limits.
Many people had been concerned about safety on the lake for a long time, Ms Bennett said.
"[Our concerns] got the rules changed, it's made it a bit safer but not totally safe, not enough because this has happened," she said.
"This is a tiny lake. It's very narrow and it has a blind corner."
She understood yesterday's incident occurred on that corner.
NZME understand that the lake's boating rules stipulate that no more than three boats are allowed on the lake at one time, and are not allowed on until after 3pm.
One local, who did not wish to be named, said the rules are widely posted around the area, but boaties "don't take any notice".
There were more than three boats on the water yesterday afternoon, she said.
"There were kids and families having a great time down there. They had kayaks, canoes, little inflatable boats and everything else... it was very sad," she said.
"It's too small a lake, I hope they ban boats altogether. I'm too devastated."
