With rest and rehabilitation, Dickson is projected to return in time for the Sept. 10 season opener against the Cincinnati Bengals at M&T Bank Stadium.
The Ravens had already taken a hit at the position when Dennis Pitta broke his right hand, underwent surgery and was declared out for the entire preseason.
Now, they'll likely need to seek reinforcements to bolster depth for the preseason.
The Ravens' top two healthy tight ends on the roster are former fifth-round pick Davon Drew and former St. Louis Rams starter Billy Bajema, who caught a touchdown from Curtis Painter against the Falcons.
Meanwhile, it's feared that defensive end Ryan McBean broke his left ankle against the Falcons when his leg got rolled up from behind by two players.
McBean is already suspended for the first three games of the regular season for a violating of the NFL's performance-enhancing drug policy.