The beige undershirt, with an "N" embroidered inside the neck and its right sleeve cut short, is expected to fetch between $500,000 (281,700 pounds) and $900,000.
Other Nelson relics and rare letters, including a 10-page epistle to his mistress Emma Hamilton, will be placed on the auction block as part of a collection celebrating the 200th anniversary of the Battle of Trafalgar.
The one-armed, one-eyed admiral became a national hero after repelling the French and the Spanish in the legendary battle that ended Napoleon's chances of crossing the English Channel.
"Anyone who beats the French usually goes down well," said Michael Grist, the Sotheby's expert in charge of the sale. "In one battle, in one day, he literally saved England. And that's the reason he's atop a statue in Trafalgar Square."
An unpublished letter discussing his naval plans three days before the Trafalgar battle could fetch as much as $54,000, while the letter to his beloved Emma could command as much as $108,000. The items are on display in New York over the weekend before their sale in London on October 5.
Nelson remains a figure of enduring fascination 200 years after he was killed in the Battle of Trafalgar, Grist said.
"He was remarkably brave in battle, but he also wanted recognition for this, and was remarkably weak in his personal life," Grist said. "He'd face the French and Spanish fleet much easier than he would face his first wife."
