Correctional Services spokesperson Mandla Sibiya said the decision was taken after consultations with stakeholders such as the ministries of health and justice.
“The ban is indefinite,” Sibiya told journalists on Monday.
The official said relatives should however continue to bring inmates necessities such as toiletry, which they would be allowed to drop at the prisons.
Local prisons are home to over 4,000 juvenile and adult inmates, both convicted and awaiting trial.
eSwatini has one confirmed case of coronavirus involving a 33-year-old female patient who is on treatment at the Lubombo Referral hospital.
On Sunday Health Minister Lizzie Nkosi announced seven new suspected cases involving people who were in contact with the confirmed case.
She said the ministry was awaiting results of the new cases.