Klaas-Jan Huntelaar's first-half strike proved enough to take Schalke up to seventh in the Bundesliga, but the loss of Draxler to an apparent hamstring injury after just 10 seconds took the shine off things.
With a key UEFA Champions League trip to Sporting Lisbon to come on Wednesday, Di Matteo will hope the winger's problem is not too serious.
Huntelaar broke the deadlock at the Veltins-Arena after 37 minutes with a close-range finish from Atsuto Uchida's cross, capping a spell of dominance from the hosts.
The Dutchman had a chance to double Schalke's advantage on the hour mark, but saw his shot from inside the box blocked.
Augsburg, who were 2-0 winners over Freiburg last time out, rarely threatened the hosts' lead, with Raul Bobadilla's wayward long-range effort compounding their frustration.
Indeed, the visitors almost conceded a second three minutes from time, Jan-Ingwer Callsen-Bracker indebted to goalkeeper Marwin Hitz for sparing him the embarrassment of an own goal.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.