Revd Mpho Tutu has said her 83-year-old father has been responding well to a two-week intravenous antibiotic course.
"The family remains concerned, obviously, and keen to see him home to rebuild his strength. We hope that he will be able to return home at the end of next week," Revd Mpho Tutu told reporters in Cape Town.
The South African anti-apartheid activist was admitted to hospital for the second time in a month for treatment of an "inflammation".
Tutu has been fighting prostrate cancer for 18 years and was released from hospital earlier in August after being treated for a recurring infection.
Last week, Revd Mpho said Archbishop Tutu was taking longer to recover every time an illness hits him, but the current infection was unrelated to the cancer.
"The series of treatments that he has had over the years have also had an impact on the elasticity of his body and his ability to come back from an illness."
Tutu retired from public life in 2010 but the Nobel peace laureate has remained outspoken on a range of issues, including gay rights and corruption in South Africa.
