McCoy is expected to be sidelined six-to-nine months.
McCoy went limping off the field late in Monday's OTA that was open to the media. Trainers examined his ankle on the field before using a cart to take him into the team's practice facility. Coach Pete Carroll had limited information after practice ended and believed it was an ankle injury.
McCoy, who plays in double tight end sets with Zach Miller, had 18 receptions for 291 yards and three touchdowns last season. The 2011 sixth-round pick also played in all 16 games during his rookie campaign.
The Seahawks addressed the tight end position in last month's draft, selecting Luke Willson in the fifth round.
Information from ESPN NFL Insider Adam Schefter and The Associated Press was used in this report.