The England batsman will miss “several” Royal London Cup matches, starting with Friday’s opener against Durham at Chester-le-Street.
“We ask that his privacy be respected during this time,” said a club statement.
With no official vice-captain in place, Steve Patterson will captain the team in Ballance’s absence.
Last week, England Test captain Joe Root led Yorkshire in their County Championship game against Surrey at the Oval when Ballance was taken ill with what was described as “a bug”.
Root is unavailable due to the international season that starts next Thursday, along with county team-mate Jonny Bairstow.
Andrew Hodd will take the wicketkeeping gloves at Durham, while pace bowler Ben Coad returns after ankle soreness/fatigue forced him out of the match at the Oval.
Coad played in the Second XI Trophy win over Derbyshire earlier this week, taking 1-8 off six overs.
Joining Adil Rashid in the 13-man squad is fellow spinner Azeem Rafiq, while batsman Tom Kohler-Cadmore also hopes to make his first appearance of the county season.
Yorkshire (from): Bresnan, Brook, Coad, Hodd, Kohler-Cadmore, Leaning, Lyth, Patterson (captain), Pujara, Rafiq, Rashid, Shaw, Wainman.