The respective bosses clashed in a violent outbreak after Sadio Mane’s aerial challenge over Takehiro Tomiyasu in a tense first half on Merseyside.
Arteta appeared to believe Mane grabbed Tomiyasu with an elbow, while Klopp resisted protests from his counterpart.
Only the fourth official separated the duo as they barked angrily at each other while coming face to face on the sideline, with an enraged Arteta even being dragged by his assistant.
Both managers were quickly given yellow cards from referee Michael Oliver, appearing to exchange more angry words as attention turned to the action on the pitch.
The Reds turned the screw in the second half, securing a four-goal victory thanks to Diogo Jota, Mohamed Salah and Takumi Minamino.