Devon and Cornwall Police say the men, aged 30 and 33, and from the Manchester area of northwest England, were arrested Monday morning near Stone's house in Cullompton, southwest England after residents reported a suspicious-looking vehicle.
Detective Inspector Steve Parker said the men "had in their possession information relating to an individual in the Cullompton area and items which lead us to suspect that they may have intended to commit a criminal offense."
The force would not confirm a report in The Sun newspaper that the men had swords, rope and a body bag, as well as maps and aerial photos of Stone's secluded property.
Parker said it was "important to stress that no properties have been burgled and no individuals have been harmed."
Police officers stood guard Wednesday outside the gates to the house, which is on a quiet country road.
Stone's London publicists, DWL, said the singer was aware of the arrests and was being kept up to date by the police.
They would not say whether 24-year-old Stone was at home when the men were arrested.
The men were being questioned Wednesday at a police station and have not been charged.
Stone came to fame in 2003 as a small-town teenager with a big, soulful voice, showcased on her best-selling debut album The Soul Sessions.
She has also taken acting roles, including that of Henry VIII's fourth wife, Anne of Cleves, in TV drama "The Tudors."
With a fortune estimated last month by the Sunday Times Rich List at 9 million pounds ($14.6 million), she still lives in the southwestern county of Devon where she was raised.
She is a friend of Prince William and was a guest at his wedding to Kate Middleton in April.