The Uruguayan manager is temporarily removed from his duties, with reports suggesting that he could leave the Championship club after failing to reach the play-off final
Assistant boss Mauricio Taricco and first-team coach Charlie Oatway have also been temporarily removed from their posts while the situation is dealt with.
"Brighton & Hove Albion has confirmed that it has suspended its manager, assistant manager and its first-team coach from their duties," read a statement on the club's official website.
"The club will now follow its internal procedures with regard to this matter and will make no further comment at this time."
The 45-year-old was close to becoming Reading manager when the Royals fired Brian McDermott in March but opted against the move, Nigel Adkins eventually being appointed at the Madejski Stadium.
After Brighton were defeated in the Championship play-off semi-final by rivals Crystal Palace, reports of the Uruguayan's exit have re-emerged, with the vacant Everton post suggested as well as potentially replacing Martin Jol at Fulham.
Poyet is understood to have differences with the board over their budgets for the coming season as they renew their attempts to reach the Premier League.