Flowers, who leads the team with six sacks, has been limited all week in practice with injured ribs. He was listed as questionable on Friday.
The 24-year-old sustained the injury in the third quarter of last Sunday's 35-17 victory over the reeling Miami Dophins.
Flowers has recorded 46 tackles in 11 games this season for the Patriots (9-2), who have won seven in a row.
Also on Saturday, New England promoted defensive lineman Geneo Grissom and wide receiver Bernard Reedy from its practice squad. The team then released defensive lineman Ricky Jean Francois and offensive lineman Jason King from the 53-man roster.
Grissom was signed by New England to the practice squad on Nov. 11 after being released from the 53-man roster two days earlier. The 6-foot-4, 265-pounder has appeared in 29 games as a reserve over the last three seasons and registered six tackles on defense and six special teams tackles.
Reedy was signed by New England to the practice squad on Nov. 22. The 26-year-old played in nine games this season for Tampa Bay and caught two passes for 21 yards and had three carries for 17 yards before being released on Nov 17.
Jean Francois, 31, made three tackles in three games with the Patriots after being signed to the 53-man roster on Nov. 7.
King, 24, was originally signed by the Patriots on May 5 before being released prior to the start of the regular season. The 24-year-old was then signed -- and released -- from the Patriots' practice squad and joined the Baltimore Ravens before being released and signed again by New England on Tuesday.