Mirallas sparked a half-time confrontation at the Emirates Stadium when the Everton midfielder appeared to squirt water at Wilshere as the players made their way off the field.
Wilshere, just back from a six-week injury lay-off, reacted angrily and Everton players stepped in to prevent a direct confrontation.
However, referee Neil Swarbrick did not feel the incident warranted further action, so neither player will face sanction.
Given the Gunners still have to face Manchester United in a five-game battle for a Champions League spot, the news will come as a welcome relief to Arsene Wenger, who was critical of Everton's robust approach after the goalless draw.
The loss of two points was a setback to Arsenal's chances of making the top four, but midfielder Aaron Ramsey has challenged his team-mates to bounce straight back on Saturday's trip to Fulham, where they could move five points clear of rivals Tottenham, who would have played two matches fewer ahead of their Sunday clash with FA Cup finalists Manchester City at White Hart Lane.
Midfielder Ramsey said: "It is important (to get a five-point gap). We always knew this week was going to be a big one for us. We are still unbeaten in a load of games and hopefully we can finish the week off strongly by getting a win against Fulham. That will put us in a strong position."
Ramsey continued: "It was important for us not to lose against Everton. It didn't quite happen for us in the final third, but overall we were quite solid. We're looking forward to the weekend.
"We still have a lot of confidence. Tottenham and Chelsea still have tough games. Teams are going to drop points and we are still positive and confident that we can finish in the top four.
"We are third at the moment and Chelsea and Tottenham may feel a bit of pressure going into their games to get the three points. The squad is going to be important for us now. Hopefully everyone will stay fit and we can finish the job off."