Councillor Simon Jones, who represents Shawbury, had been Shropshire Council's cabinet member responsible for adult social care and public health.
The authority confirmed that he will be leaving the post temporarily, with his responsibilities taken on by two other current cabinet members.
A statement from the authority said: "Simon Jones is stepping back from his cabinet responsibilities covering adult social care and public health, due to suffering long-term effects following contracting Covid-19 earlier this year.
"His responsibilities are now being shared on a temporary basis between cabinet members Cecilia Motley (adult social care and public health) and Dean Carroll (housing)."
Lezley Picton, leader of Shropshire Council, said: “We all wish Simon a speedy recovery, and hope that he will be back soon. I am very grateful to Cecilia and Dean for looking after his areas in the meantime.”