The Germany international has not played for the club since December's Champions League win over Basel, having picked up the problem in January.
However, Draxler, linked heavily with a move to Arsenal during the transfer window, began running again on Sunday before continuing his recovery a day later.
"Julian Draxler is back on the pitch. After the 20-year-old had run laps in the park stadium on Sunday, he was also back on the pitch on Monday," a statement on the club's official website read.
"Draxler will, in the coming days, intensify his training program piece by piece and then work on his comeback in team training.
"When exactly the midfielder will rejoin the team, however, is still unclear."
Draxler is reported to have come close to moving to the Emirates Stadium in January, stating recently that Schalke's general manager Horst Heldt "had offers" for him.