Pepe was sent off during the 0-0 draw after appearing to headbutt Alioski in response to an apparent provocation, with the Ivory Coast winger dismissed early in the second half to leave Arsenal clinging on to a point.
The Ivory Coast international was spotted by television cameras thrusting his head towards Macedonian winger Alioski shortly after the start of the second half as they clashed in the 50th minute, with referee Anthony Taylor issuing a straight red card in the 51st minute following a VAR review for violent conduct.
An Arsenal club statement read: “We utterly condemn the vile abuse directed at Nicolas Pepe and Ezgjan Alioski on social media following our match against Leeds United.
“This is completely unacceptable and we will be working with the police and authorities to do everything we can to trace and prosecute the culprits.”
Leeds United said: “The vile abuse directed at Ezgjan Alioski and Nicolas Pepe on social media after yesterday’s Premier League game with Arsenal will not be tolerated by Leeds United.
“We will work closely with the police and the footballing authorities to ensure those responsible are identified and punished.”
Arsenal manager Mikel Arteta was left far from impressed with Pepe’s conduct, with the 25-year-old now set to miss their next three Premier League games against Wolves, Tottenham and Burnley through suspension.
Arteta repeatedly said Pepe’s behaviour was “unacceptable” following the match and that he had “let down” his teammates, though he refused to discuss the matter further after speaking with Pepe in the Arsenal dressing room.
Alioski was also involved in a second incident after the final whistle when he was confronted by an irate Kieran Tierney, with the Arsenal left-back taking exception to his reaction in what he appeared to suggest was an over-the-top attempt to get Pepe sent off. Tierney had to be restrained by his teammates and dragged away from Alioski as he remonstrated with the 28-year-old Leeds midfielder.