Oladipo, a second-year guard, sprained the medial collateral ligament in his right knee after landing awkwardly during a scrimmage on Friday. Frye, a free agent pickup, suffered the same injury in his left knee during a scrimmage.
Both players will miss Tuesday's preseason opener against Miami.
Oladipo was able to finish Friday's scrimmage, but was sent for an MRI on Saturday after reporting soreness.
"This could have been way worse, so I'm lucky," Oladipo said Monday. "I'm just going to heal up and prepare mentally so that when I come back I won't be a step behind. Hopefully, it will be a step forward.
"It is what it is, I'm taking it one day at a time and based on the treatment we'll see when I'll be able to come back."
Orlando also will be without guard Willie Green, who is listed as day-to-day with a hyperextended left knee. Green was acquired off waivers in June.
The Magic have only six players on their preseason roster that were on the roster to begin the regular season a year ago.
"It gives an opportunity for other guys to understand how we want to play," Vaughn said. "It's not ideal and we'd love to have all 15 guys ready to rock and roll, participating and learning each other, but that's not where we are. But you know we won't complain and we'll keep this thing rolling."
The Associated Press contributed to this report.