The New Zealander oversaw Ireland's superb 26-23 victory over Australia at the Aviva Stadium on Saturday despite suffering with symptoms of appendicitis.
After the game Schmidt went for tests at a hospital in Dublin and subsequently had an operation to have his appendix removed.
"Following [Saturday's] game against Australia, Ireland head coach Joe Schmidt was assessed by the matchday doctors and was sent to St Vincent's Hospital for further assessment," read a statement from the Irish Rugby Football Union.
"On Saturday night Joe had his appendix removed and is recovering well this morning [Sunday].
"He would like to thank the doctors and nurses of St Vincent's Hospital and everyone for their well wishes and kind messages of support."
Ireland's victory completed a clean sweep of wins during their November internationals, including the notable scalps of the Wallabies and South Africa.