The girl, named by local media as Saga Vanecek, said she had been "throwing sticks and stones and stuff to see how far they skip".
"I'm not sure you should be touching it anymore", he replied.
Saga Vanecek was helping her father with his boat in the Vidostern lake when she stepped on an 85cm (34in) sword in a holster made of wood and leather.
"Indeed an fantastic story!"
Find Saga has prompted local authorities to begin research in the lake and on its shores.
According to the museum, the sword is about 33 inches long and "exceptionally well-preserved".
Swedish-American Saga Vanecek found the ancient artifact while playing in Vidöstern lake during the summer near her family's holiday home in the south of the country.
Mikael Nordström, an expert from the Jonkopings Lans Museum, described the discovery of the relic as spectacular, saying that it was "about 85 centimeters long, and there is also preserved wood and metal around it".
This brooch was found when the site was searched.
For now, the sword won't be available for display since it has to undergo a preservation process that could take up to a year.
"Why it has come to be there, we don't know", he said.
Saga grew up in Minneapolis and moved to Sweden just a year ago, USA Today reports. "At first we thought it could be graves situated nearby the lake, but we don't think that anymore".
For Saga's father, the discovery was very fitting being a native Minnesotan.
"That it was pretty cool and that it was exciting", she told Radio Sweden.
"As she held it high, gravity bent the fragile, over thousand year old weapon, and it was then that [I] realised that it actually was a sword."