The 20-year-old Austrian footballer of the year, a key player in Bayern's run to the Champions League final last season, had a 20-minute individual training session on Friday and is set to gradually join team training, Bayern said In a statement.
They did not, however, set a date for the midfielder's return.
Holger Badstuber has been shifted from central defence to the left in Alaba's absence - he has been playing at left-back for the past six months.
Bayern, top of the Bundesliga after three wins in three games, travel to Schalke 04 on Saturday.
- Sports & Recreation