Rudy, who joined on a free transfer in July after his contract expired at Hoffenheim, has impressed at the base of the German champions' midfield in the absence of the retired Xabi Alonso.
The 27-year-old set up Niklas Sule to open the scoring in the 3-1 win over Bayer Leverkusen and delivered strong displays in the DFB-Pokal thrashing of Chemnitzer and the DFL-Supercup penalty shoot-out win over Borussia Dortmund.
And Ribery believes he brings the sort of qualities to the side that Kroos did during a hugely successful Bayern career before he joined Madrid in 2014.
"I've always thought: good player, quiet, but not shy. He is not afraid when he's on the pitch," Ribery told Bild.
"Rudy is a bit like Toni Kroos - his style is similar."
The veteran winger also expects Sule to prove a good signing for Bayern.
"I will definitely have no problem with Sule," he said of the centre-back, who arrived from Hoffenheim for a reported fee of €25million.
"He knows Bayern is a different level. He's still young but he's a good player. He has character and he's brave. I like that."
Bayern travel to Hoffenheim in the Bundesliga on Sunday (AEST).