The club have confirmed that the 52-year-old flew out to Barcelona to for "emergency surgery" carried out by Dr Mireia Illueca, and he will recover in Catalonia following a successful operation.
The Citizens have also revealed that assistant coach Juanma Lillo will take charge of all first-team training duties and the club's next two Premier League fixtures before the international break.
A statement from the club's official website read: "Pep Guardiola has today undergone a routine operation on a back problem.
"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.
"Everyone at Manchester City wishes Pep a speedy recovery, and look forward to seeing him back in Manchester soon."
Lillo only rejoined Guardiola's backroom staff at the beginning of this month following a spell as head coach at Qatari club Al-Sadd.
The 57-year-old will now oversee coaching duties of the first team for Sunday's Premier League fixture away against Sheffield United at Bramall Lane, as well as the home encounter with Fulham on September 2.
Should Guardiola make a full recovery during the international break, the City boss could return to the touchline for the Premier League trip to the London Stadium against West Ham United on September 16.
Man City have made a perfect start to the new Premier League season under Guardiola, claiming victories without replay against Burnley and Newcastle United - beating the latter 2-0 at the Etihad Stadium last Saturday.
The treble winners also won their first trophy of the new season last week, beating Sevilla 5-4 on penalties to lift the UEFA Super Cup following a 1-1 draw in 90 minutes in Athens.
Guardiola has won at total of 15 trophies during his exceptional seven-year reign as Man City manager, guiding the Citizens to 308 victories in 417 matches across all competitions.