Browns coach Freddie Kitchens confirmed Ogbah did not report on Monday.
"Ogbah didn't show, and I'd rather talk about the guys that are here. I'm sure he's got his reasons. I don't know," Kitchens said.
Kitchens also said running back Duke Johnson was not present Monday. His status has been questioned since the Browns signed Kareem Hunt, but Kitchens said last week that there is a role for Johnson on the team.
Asked if Johnson's absence was related to Hunt's signing, Kitchens said: "I don't know. You have to ask Duke that. I'm not speaking for Duke. He chose not to be here, and he has the ability to do that. It's voluntary."
The Browns also have waived receiver Ricardo Louis, who missed last season with a neck injury, and safety Derrick Kindred. When Ogbah is traded, only three players will remain from the 14 taken in the 2016 draft.
Teams with new coaches were permitted to begin Phase 1 of their offseason programs on Monday. Attendance for this phase of the program is voluntary, although most players attend.
Ogbah, 25, was drafted in the second round (32nd overall) of the 2016 draft and has 12.5 sacks in three seasons with the team. He started all 40 games he has played in for the Browns
In 14 games last season, he finished with three sacks and 40 tackles.
Kindred, 25, had 33 solo tackles, an interception and a forced fumble in 16 games for the Browns last season. Drafted in the fourth round in 2016 (129th overall), he appeared in 42 games with the Browns, including 17 starts.
Louis, 25, had 45 receptions for 562 yards in 32 games with the Browns, including 12 starts, since being selected in the fourth round (114th overall) of the 2016 draft.
In addition to Louis and Kindred, other players drafted in 2016 who are no longer with the team include receiver Corey Coleman (Round 1), defensive end Carl Nassib, quarterback Cody Kessler, receiver Jordan Payton, offensive lineman Spencer Drango, cornerback Trey Caldwell, offensive tackle Shon Coleman and linebacker Scooby Wright.
In other moves Monday, the Browns signed free-agent defensive back Juston Burris and two exclusive-rights free agents -- defensive lineman Trevon Coley and defensive back Jermaine Whitehead. The team also waived defensive back Howard Wilson.
ESPN's Pat McManamon contributed to this report.