Hoeness pleaded guilty to tax evasion earlier this week and resigned his post on Friday after being sentenced to three and a half years in prison.
The 62-year-old first joined Bayern as a player in 1970 and had been with the club ever since, taking over the presidency role in 2009 and overseeing some of the most successful years in their history, including lifting the Champions League last season alongside a domestic league and cup double.
Bayern played their first match without Hoeness on Saturday, beating Bayer Leverkusen 2-1, and Guardiola, who was persuaded to take charge of the team by the former president, hopes he will return to the post some day.
"I've only been here nine months, but I've seen enough to realise that Uli is extremely important here," Guardiola told Sky television.
"He's made a mistake and he has admitted to it. I hope I can still be here when he comes back."
Club chairman Karl-Heinz Rummenigge feels the club must now focus on retaining their status as the team to beat in Germany and Europe.
"I wish him all the best," he said. "Of course we are all very sad because we are partners who have shaped Bayern Munich together over many years.
"Uli Hoeness was a man who formed Bayern extremely positively over decades. Uli certainly has a great deal of the merit for the club being in the position they are in now.
"We've now got to try to ensure that the club remains stable. It's not going to be simple because you can't just replace a man like Uli."
On the field, Bayern moved to within potentially one win of clinching the title.
Victory at Mainz next Saturday and favourable results elsewhere would see Bayern pick up the Bundesliga with a record-breaking eight games to spare.
"We only need a few points now," said Guardiola. "It's not important when (we win it), but that the players keep this positive tension."