McGlinchey's status came into question when the tackle was not seen at the start of Wednesday's practice.
The injury occurred during Monday night's 31-3 victory over the Cleveland Browns. McGlinchey will be replaced by Daniel Brunskill at right tackle. The team also re-signed Sam Young on September 20.
"[The injury to McGlinchey] happened in two plays, I think," Shanahan told reporters. "It started on one, and then got worse on another."
Shanahan noted that the severity of the injury was a surprise to both the 49ers and McGlinchey, who fought to return to the game on Monday night following the injury.
"They fell on his legs awkwardly, and it's an unfortunate injury," Shanahan said.
The 49ers are already without veteran left tackle Joe Staley, who is recovering from a fractured fibula. Justin Skule has been playing in place of Staley.
Shanahan said the 49ers currently have no plans to trade for another tackle. The team also has no plans to cut someone from the 53-man roster to add a player or elevate someone from the practice squad.
"Brunskill has got in a little bit," Shanahan added, "a couple of plays here in the last two weeks. So at least he's gotten in there a little bit. He had a real good preseason, so I know he'll go in and do a good job."
McGlinchey is in his second NFL season. He played college football at Notre Dame, and the 49ers made him the No. 9 overall pick last year. McGlinchey has started every game (20) of his pro career.
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