Hawley, 25, was carted off the field during the Falcons' Week 4 loss to the Minnesota Vikings with a right knee injury He was a fourth-round pick by the Falcons in the 2010 NFL draft.
Holmes, 25, injured his foot against the Vikings. He was a third-round pick by the Falcons in the 2012 draft and had started all four games for Atlanta this season.
The Falcons were already playing this season without starting left tackle Sam Baker, who was lost for the year in the preseason due to a torn patella tendon.
Hawley and Holmes had been key parts of the offensive line that has protected quarterback Matt Ryan well during the team's 2-2 start. In four games, Ryan has been sacked just five times and is second in the NFL in passing yards.
Atlanta's 444 total yards per game are tied with the Indianapolis Colts for first in the league.
The Falcons also placed safety William Moore on injured reserve/designated for return with a shoulder injury. He will be eligible to return to practice in six weeks and play in games in eight weeks.
Moore was a second-round pick in the 2009 draft and has 14 interceptions the past four seasons, including three last season. He has nine tackles and one forced fumble for the Falcons this season.
The Falcons rank 31st in the NFL in defense, allowing 429.8 yards per game. They've allowed the third-most passing yards in the league and are tied for 20th in interceptions with just two.
The team also on Tuesday signed offensive tackle Cameron Bradfield and promoted guard Harland Gunn and safety Sean Baker from the practice squad.
Atlanta travels to New York to play the Giants on Sunday at 1 p.m.
- Paul Palladino