Assistants Mauricio Taricco and Charlie Oatway have also been instructed to stay away from the Championship club.
It is reported that Poyet told his players of his intention to leave Brighton following the club's Championship play-off semi-final defeat to arch-rivals Crystal Palace.
The Uruguayan has been linked with a possible move to both Fulham and Everton.
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 took Brighton into the Championship into 2011.
- Sports & Recreation
- Charlie Oatway