Skriniar, whose contract expires at the end of the season, has agreed to join Paris Saint Germain as a free agent this summer.
The Slovakia international has been skippering Inter for much of this season after substantive captain Samir Handanovic lost his position to Andre Onana.
But ahead Sunday's Milan derby against AC Milan, manager Simone Inzaghi has revealed Skriniar is no longer a part of Inter's captaincy group even though he is in contention to start the game.
"We have hierarchies based on appearances, but because of what happened he will no longer be the captain," Inzaghi said at Saturday's pre-match press conference.
"We talked about it very calmly with the club and the boy.
"The captain is Handanovic, then we'll scale based on appearances with [Marcelo] Brozovic, [Danilo] D'Ambrosio and Lautaro [Martinez].
"The thing that matters most to me is the match."
"I don't judge his choices but the man and the player, who are unique," Inzaghi said of Skriniar. "He is a splendid boy, who works very well every day. He will probably be a starter."
Skriniar has won one Serie A, one Coppa Italia and two Italian Super Cups since joining Inter from Sampdoria in 2017.
