"I had a minor scope done on my right knee. I'll be back to full speed in two weeks. Better to get it taken care of now," he wrote.
An Eagles spokesman told USA Today Sports that the team expects Casey to be ready for training camp.
Casey signed a three-year, $14.5 million contract with the Eagles this offseason. The Eagles signed tight end Will Shaw this week after waiving running back Miguel Maysonet, likely to help fill the void left by Casey's injury during OTAs.
The Eagles drafted tight end Zach Ertz in the second round of the 2013 draft, but he is not allowed to participate in OTAs per NFL rules until his class graduates from Stanford in June.
The Eagles already feature veteran tight end Brent Celek, who has been their primary starter for the past four seasons. However, coach Chip Kelly is expected to feature multiple-tight-end sets in his up-tempo Eagles offense.
A versatile player who also can line up in the backfield, the 6-foot-3 Casey has spent his entire four-year career with the Houston Texans, where he was used primarily at fullback.
Casey, 28, had 34 catches for 330 yards and three touchdowns -- all career highs -- last season with Houston. The 235-pounder has hauled in 66 career receptions in 61 games.
Information from The Associated Press was used in this report.