Zuma's statement said Mandela "continues to receive high care" at his home in the Houghton suburb of Johannesburg and that "his daily routine is being gradually re-established."
Zuma congratulated Mandela on his recovery and said the anti-apartheid icon has "the love and support of all South Africans."
Mandela has been reading newspapers, sitting up in bed and receiving visitors, according to reports in the South African media.
The news that Mandela has recovered from the recurring lung infection and the minor surgery will reassure many in South Africa concerned about the aged leader's health.