The pair clashed during the first half of Hull's Premier League fixture against Sunderland at the KC Stadium on Tuesday.
Poyet was initially sent to the stands by referee Mike Dean after booting a container full of drinks into the air.
The Uruguayan was showing his disgust at a decision that saw Jack Rodwell booked for simulation in the 36th minute. Television replays proved Dean's call was correct.
After disputing the decision, Poyet walked over to Bruce and appeared to look for a handshake, only for the Hull manager to react furiously.
Bruce tried to run at Poyet and had to be restrained by match officials as the angry Sunderland head coach made his way up the tunnel.
The FA could take a dim view of an incident that marred the first half of Tuesday's fixture.
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