The Austrian international partially tore his medial ligament and damaged the meniscus in his right knee in Bayern's 2-0 win over Roma in the group stages of the UEFA Champions League, with the injury requiring surgery.
The defender returned to Bayern's Sabener Strasse training centre on Monday, completing a set of sprinting and running drills in football boots before switching to running shoes for 30 minutes of jogging.
The rest of the squad are not required to report back for duty until January 7 but Alaba returned early in an attempt to boost his chances of being fit when the Bundesliga restarts at the end of the month.
Holger Badstuber, Medhi Benatia and Pierre-Emil Hojbjerg joined Alaba in practice, as well as goalkeeper Tom Starke.
Bayern's only remaining long-term absentees from the first team are captain Philipp Lahm and midfield duo Javi Martinez and Thiago Alcantara.
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1
