Lahm opted to retire from international football after leading his side to World Cup glory in Brazil this summer, having first taken up the armband for the finals in 2010.
Schweinsteiger was vice-captain to his Bayern Munich team-mate in Brazil and Beckenbauer believes the 30-year-old is the obvious choice to take up the armband.
"Schweinsteiger for me is the logical successor to Philipp Lahm," he told Bild. "He's a leader, he won a lot of sympathy for his incredible versatility in the World Cup final.
"The whole team is raised by such a fighter. And, as deputy to Lahm, he knows the captain's role already."
Beckenbauer feels Mats Hummels would be the ideal deputy to Schweinsteiger, while he claims Manuel Neuer would not be the correct choice given his position on the pitch.
"[Hummels] should be vice-captain to Schweinsteiger. Neuer is a great personality, but a coach prefers an outfield player as they can better influence the action," he added.