Daniels bent his elbow backward while tumbling from an accidental stamp by his own guard in the first half of Sunday's loss to the Dallas Cowboys, and was carted off the field with a towel covering his head.
The 25-year-old quarterback had already dislocated the same joint last year, and after undergoing imaging on Monday will see specialists this week to assess the full damage and prospects for recovery, said Quinn.
Initial X-rays taken immediately following the gruesome-looking injury had shown no bone fracture.
"As far as the specialists go and what they see and what they think, I don't have an answer regarding that yet," said Quinn.
Daniels steered Washington to within a game of the Super Bowl in his thrilling 2024 rookie season. But the following campaign was severely hit by injuries, including to his left elbow.
Backup quarterback Marcus Mariota made 11 appearances and eight starts in 2025, and will again deputize for Daniels in the Commanders' clash Sunday with reigning NFL champion Seattle, said Quinn.
But the Washington coach rejected any suggestion that Daniels is unusually injury-prone.
"The freak (injuries) like this, it's hard to explain honestly," said Quinn.
"There's re-injury for all things, whether it's soft tissue or otherwise. But he really put on more armor this year, and worked hard during the off season for that. He's bigger, he's stronger."
Elsewhere, Chicago Bears coach Ben Johnson said quarterback Caleb Williams had received a "somewhat encouraging" medical report after suffering a hamstring injury during Sunday's loss to the Minnesota Vikings.
Williams pulled up in agony while scrambling in the red zone late in the game.
"We're saying week-to-week with him right now. We'll see where he's at as the week progresses, and how long that means," Johnson told a press conference Monday.
Williams is not expected to practice this week, but is not yet ruled out for Chicago's clash with Philadelphia next Monday, the coach added.
There was happier news for Minnesota's first-choice quarterback Kyler Murray, who missed Sunday's game after suffering a concussion in a clash with Green Bay Packers a week earlier.
"Head Coach Kevin O'Connell has announced QB Kyler Murray has cleared the concussion protocol and will start Sunday at Tampa Bay," said the team, on social media.
During Murray's absence, backup QB Carson Wentz led the Vikings to two wins and a surprising 2-0 start.
And Michael Penix Jr. will return from his 10-month injury layoff as the starting quarterback for the Atlanta Falcons this Thursday against Green Bay, the team announced in a statement.
Penix underwent surgery last November for a torn ACL.
Cooper Rush stood in for Atlanta's first two games this season. The Falcons lost both and failed to even reach the red zone in either.