The German international captained the Die Roten side to a historic Treble last season as Jupp Heynckes's side won the Bundesliga, the Champions League and the DFB Pokal.
Carragher wrote in his column in the Daily Mail: "I would like a defender to win [the Ballon d'Or] for the first time since Fabio Cannavaro in 2006. Step forward Philipp Lahm.
"He captained the Treble winners, broke through the 100-cap mark for Germany and this year and has been the best full back in the World.
"At 29, he is operating at the peak of his powers and there would no more deserving winner."
Lahm has recently moved from his traditional full-back role to a central midfield position under Bayern coach Pep Guardiola.