Luiz, who scored in the quarter-final last Friday, will wear the captain's armband for the clash in Belo Horizonte.
Carragher wrote in his column for the Daily Mail: "Like many Brazilians, Dante can be blase with the ball at his feet and is sometimes too casual - he can give a forward a chance, but he's no average understudy.
"He was part of a Bayern defence that conceded only 23 goals in 34 league games last season and finished with a goal difference of +71, winning the title in March.
"Brazil have got this far because of the goals from their central defenders. Dante and Luiz will need to be outstanding on Tuesday to keep up their progress."
The other semi-final between the Netherlands and Argentina will take place on Wednesday.