The Germany international has not played for the club since December's Champions League win over Basel, having picked up the problem in January.
But Draxler 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."
Arsenal dispatched a delegation to Germany in the final week of the January window to negotiate a deal for Draxler, but refused to meet the Schalke star's £37.2 million release clause.