Wenger was angered when Mourinho leapt from the dug-out to remonstrate after Arsenal forward Alexis Sanchez went down under a challenge from Gary Cahill mid-way through the first half, and pushed the Portuguese in the chest.
The two men were separated by referee Martin Atkinson, but continued to exchange words afterwards.
The provocative Mourinho is no stranger to controversy, while Wenger has been involved in similar incidents with Alan Pardew, who was managing West Ham United at the time, and former Tottenham Hotspur coach Martin Jol.
Meanwhile, Chelsea goalkeeper Thibaut Courtois was forced to go off in the first half of his side’s game against Arsenal on Sunday after injuring himself in a collision with Sanchez.
Sanchez’s hip slammed into the side of Courtois’s head as the Chilean forward chased Jack Wilshere’s pass into the Chelsea box in the 10th minute of the Premier League game at Stamford Bridge.
Courtois continued playing after receiving treatment, but he was eventually obliged to give way to Petr Cech in the 24th minute, with television pictures showing blood running from his right ear.
A Chelsea spokesman said that Courtois had been taken to hospital to undergo tests “as a precaution”.
Belgium international Courtois, 22, has supplanted Cech as Chelsea’s first-choice goalkeeper this season after
spending the last three years on loan at Atletico Madrid.