The 52-year-old is back in his native Spain as he recovers from the emergency operation.
In his absence, City have announced that his assistant Juanma Lillo will take over the club's first-team duties.
And this will see Lillo be on the sidelines for the upcoming clashes against Sheffield United and Fulham.
He had only returned to the Etihad earlier this month after a spell managing Qatari side Al Sadd.
A club statement on Tuesday read: "Pep Guardiola has today undergone a routine operation on a back problem.
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"The Manchester City boss has been suffering with severe back pain for some time lately, and flew out to Barcelona for emergency surgery performed by Dr Mireia Illueca.
"The surgery was a success, and Pep will now recover and rehabilitate in Barcelona.
"In his absence, assistant manager Juanma Lillo will oversee coaching of the first team on the training field and will assume duties on the touchline until Pep's return.
"He is expected to return after the forthcoming international break.
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"Everyone at Manchester City wishes Pep a speedy recovery, and look forward to seeing him back in Manchester soon."
Guardiola heaped praise on Lillo following his return, as he remarked: "Juanma sees things no one else in the game sees.
"He understands football on an incredible level, so he is the perfect person for me to work alongside.
"I have always been inspired by him - his knowledge of football, his intelligence and his humanity mark him out as a very special person in my life - and we have a shared ideology.
"He is a friend, a colleague and an inspiration. I am so, so happy he is back here at Manchester City.
"His preparation for matches is absolutely amazing. I know he will raise standards because he works so hard every single day."