The Warwickshire seamer will replace Liam Plunkett in the 16-man squad for the five-match series as the Yorkshire fast bowler is getting married. Stone, 24, who has struggled with injury problems in recent years, has impressed selectors with his consistent displays this season.
Although Plunkett will miss the first three matches of the series, which starts on October 10 in Dambulla, he will be available again for the last two ODIs.Yorkshire all-round David Willey was not considered for selection as he continues to recover from a back injury.
The England squad will depart for Sri Lanka on September 30 and their first warm-up game takes place in Colombo on October 5. Ben Stokes and Alex Hales were both included in the squad, a day after they were charged with bringing the game into disrepute by the England and Wales Cricket Board.
The pair face a disciplinary hearing in December over an incident outside a Bristol nightclub in September last year.
Stokes denied a charge of affray and was cleared following a seven-day trial at Bristol Crown Court last month.
Full squad: Eoin Morgan (Middlesex), Moeen Ali (Worcestershire), Jonny Bairstow (Yorkshire), Jos Buttler (Lancashire), Sam Curran (Surrey), Tom Curran (Surrey), Liam Dawson (Hampshire), Alex Hales (Nottinghamshire), Liam Plunkett (Yorkshire), Adil Rashid (Yorkshire), Joe Root (Yorkshire), Jason Roy (Surrey), Ben Stokes (Durham), Olly Stone (Warwickshire), Chris Woakes (Warwickshire), Mark Wood (Durham).