The Nottinghamshire seamer will cover for Chris Woakes, who has been ruled out of the first part of the series due to a right quad strain.
Ball has not played a Test since being dropped during the Ashes defeat to the Baggy Greens last winter, but the 27-year-old has played 17 one-day internationals.
The bowler featured in England's 4-1 ODI series win over Australia in January, and he has taken 10 wickets in the One-Day Cup this season.
Ball is also the leading wicket-taker in the County Championship, with 27 at an average of 18.33 runs per wicket.
The first ODI against Australia kicks off on June 13 at The Oval.