"Harry is nursing a minor injury, just a little knock. We're not going to take any chances with it," Carsley informed the media on Wednesday.
Asked to clarify whether Kane will be on the bench, Carsley said: "We're not ruling him out yet of the game, but he won't start the game.
"Hopefully he'll be in contention then for Sunday against Finland but, again, time will tell. It's not something I think we should be rushing."
In Kane's absence, Manchester City defender John Stones will captain England for the first time on Thursday.
"It's a brilliant achievement for John. Something that he deserves. The amount of caps he's got, the experience he's got, the level of professionalism that he shows within the squad, the example he is to the younger players," Carsley said.
Ahead of his 82nd cap for England, Stones admitted it was a dream come true to lead his country at Wembley.
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'An absolute honour'
"It's definitely everything that I could have dreamed of as a kid," the 30-year-old said.
"For my family to be able to see me walk out as England captain is a special moment and one I can't thank Lee enough for.
"To be walking out with the armband on is an absolute honour and a moment I will cherish forever."
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Stones' City team-mate Jack Grealish could be sidelined against Greece after the winger sat out training on Wednesday.
"Jack just picked up a slight knock yesterday but our attitude would be we wouldn't gamble with any of the players," Carsley said.
Chelsea forward Cole Palmer was named England's men's Player of the Year this week in the latest milestone for the emerging 22-year-old, who already has six goals for the Blues this term.
Palmer is expected to continue his remarkable rise by making his first competitive England start on Thursday.
"Cole's in fantastic form," said Carsley, who enjoyed wins over Ireland and Finland in his first two games in charge in September.
"I think he's carried that into this week. He's such an exciting player, a player that I've worked with for four or five years now.
"Cole, along with a lot of the other attacking players, have put themselves into a great position to start the game tomorrow."
Greece boss Ivan Jovanovic said England are a more dynamic outfit than the side that reached the Euro 2024 final under Gareth Southgate, who quit after that painful 2-1 loss to Spain.
"Southgate did a lot for English football. However the style has changed slightly under Lee Carsley," he said.
"He has instilled a bit more of a possession-based style and the players have a bit more creative freedom.
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"Wembley is a symbol of world football but the team is not here for tourism."
(This story has not been edited by staff and is auto-generated from a syndicated feed.)