Woods and Mickelson last played together in the first two rounds of the PGA Championship at Valhalla in 2014.
They have not been in the same group at the Players Championship since 2001.
Woods has twice won the Players, while Mickelson and Fowler have one victory each.
McIlroy, Spieth and Thomas, meanwhile, have eight major titles between them, but none has won the Players, considered the next most significant event on the schedule.
The PGA Tour has not announced the full draw for the Players Championship.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Ken Ferris)
