There are no details on the nature of O'Neill's operation, who is expected to be released in the "next day or two".
The 74-year-old signed a one-year deal in June to become permanent manager after two interim spells last season culminated in a Scottish Premiership and Scottish Cup double.
"In response to speculation, we can confirm that Martin O'Neill has undergone a small procedure in hospital," Celtic posted on social media.
"We would envisage Martin being released from hospital in the next day or two and on behalf of Martin, we would like to thank supporters for their kind wishes.
"We would ask that the privacy of Martin and his family is respected."
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