The full-back complained of severe pain on the right side of his face and jaw shortly before the Premier League clash was due to kick off and was taken to hospital for tests.
Initial scans indicated a localised infection, but the England international was allowed to return home on Saturday evening and is likely to be fit for training in the week.
Medical staff at Anfield expect Johnson to be back in contention for next Saturday's Premier League clash with Fulham.
Santi Cazorla and Aaron Ramsey scored the goals as Liverpool were consigned to just their second defeat of the campaign at the Emirates Stadium.
Johnson has featured in five league games for Brendan Rodgers' men this season either side of a spell on the sidelines due to an ankle injury, with Liverpool picking up 13 points from a possible 15 in those matches.
