A nearly tennis-ball-size gem discovered in Botswana is the second-largest diamond ever unearthed, smaller only than a precious stone that furnished the British crown.

The 1,111-carat gem-quality diamond was found this week at the Karowe Mine in Botswana, said Lucara Diamond Corp., the Vancouver-based company that owns and operates the mine. It was among a cache of huge white diamonds discovered at Karowe this week, including an 813-carat stone the company said was the sixth-largest ever found. One carat is equivalent to one-fifth of a gram.

“I am truly at a loss for words,” said Lucara Chief Executive William Lamb. “We are truly blessed by this amazing asset.”

Lucara’s shares were up 27% in Stockholm on Thursday as a result of the discovery of the stone, whose value could run into the tens of millions of dollars.

The largest diamond ever discovered was a 3,106-carat Cullinan stone found in South Africa in 1905. The stone was cut into several large polished gems, including the Great Star of Africa and the Lesser Star of Africa, both of which are housed in Britain’s crown jewels.

Botswana, along with southern African neighbors South Africa and Namibia, is one of the biggest producers of mined diamonds, with Australia and Russia also important suppliers.

Numis Securities analyst Phil Swinfen said it is hard to put a value on a diamond without more details about color or the ways it could be cut. Mr. Swinfen, a former diamond-mining geologist, said the Lucara diamond could fetch between $40 million to $60 million or more based on recent sales of large stones the company has found. Lucara sold a 342-carat type IIa diamond discovered in April for $20.55 million, equivalent to $60,087 a carat.

“Given this stone is likely to be historically significant, the value could take on a life of its own and achieve significantly more—all flowing straight to Lucara’s bottom line,” Mr. Swinfen said. “This is immensely good news for Lucara, perhaps the best week in the company’s history.”