Guardiola said Rodri was “irreplaceable” during last season’s title run-in, in which City pipped Arsenal to win their fourth consecutive league title.
Rodri missed five games last season and City lost four of them.
“Unfortunately we got the worst (news) but these things happen,” added Guardiola. “We will be there to support him in his recovery step-by-step.
“What he gives us, we don’t have a similar player.
“But the others can all together replace what Rodri has given since his arrival to us. We will have to do it as a team and find a way to play a lot of matches without an important player for us.”
Guardiola said the club will assess the “potential problems” caused by Rodri’s absence before deciding whether to sign a new midfielder in the January transfer window.
Meanwhile, City are set to be without Belgium midfielder Kevin de Bruyne for their Premier League trip to Newcastle United on Saturday (12:30 BST).
De Bruyne missed the draw with Arsenal and may not return to action until after the international break in October.
City also face Slovan Bratislava in the Champions League and Fulham in the Premier League before the mid-October internationals.