Poyet, assistant manager Mauricio Taricco and first-team coach Charlie Oatway have all been relived of their duties pending an internal investigation.
The Uruguayan is believed to have had a series of disagreements with the club's board over his transfer budget for the summer.
But Brighton declined to reveal the reasons behind the suspension of Poyet, who has three years remaining on his current contract.
A club statement read: "Brighton & Hove Albion has confirmed that it has suspended its manager, assistant manager, and its first team coach from their duties.
"The club will now follow its internal procedures with regard to this matter and will make no further comment at this time."
Poyet's future on the south coast was already the subject of intense speculation linking him to a number of vacancies.
He admitted he was "considering his options" following Brighton's play-off semi-final defeat by Crystal Palace on Monday.
The 45-year-old is reportedly on Everton's shortlist to replace David Moyes when he departs to take over at Manchester United in the summer, while Stoke and Fulham are also believed to be interested.
Poyet's suspension comes on the day he was nominated for the Championship manager of the month award after the Seagulls went unbeaten in April, recording three wins and three draws to finish fourth.