Doctors have asked him to rest, and “we’ll be doing our best not to disappoint them,” his daughter Reverend Mpho Tutu said in a statement.
He thanked his medical team for their expertise and generosity, she added.
Archbishop Tutu retired from public life in 2011 but continues to travel.
The 83-year-old Nobel peace laureate cancelled a planned trip to Rome in December following another infection.
The latest infection was not linked to his treatment for prostate cancer, which has afflicted him for more than a decade.
The statement said that he returned home wearing a dressing gown with the words “Feet Up Arch” on the back – underlining the message that the 83-year-old needs to take a break.
Archbishop Tutu is now looking forward to watching a bit of cricket match between South Africa and Bangladesh in Dhaka, the statement added.