Wellington's job has come under scrutiny follow the club's inconsistent performance in the championship this season.
His absence, however, is not a result of their disappointing showing.
"The Management of Accra Hearts of Oak Sporting Club Limited wishes to bring to the notice of the general sporting public, especially Hearts of Oak fans, that due to medical condition, head Coach Henry Lamptey Wellington will be absent from Hearts’ next Premier league match against Karela F/C on Wednesday 18 April, 2018," a club statement read.
"In his absence, Assistant Coach Edward Nii Odoom will lead the team into the midweek game against Karela F/C at Anyinase.
"The Management wishes Coach Wellington a speedy recovery."
Wellington, formerly an assistant coach, was handed Hearts job shortly before the start of the season following the unexpected dismissal of Scotsman Frank Nuttall.
After seven matches in the championship, the twenty-time champions have three wins, three defeats and a draw, leaving them sixth on the table.
The nondescript performance has heightened calls for his dismissal.