Interim manager Gareth Southgate said the decision was tactical and not a reflection of the forward's form.
Rooney, who was booed by sections of the Wembley crowd during Saturday's 2-0 win over Malta, has not started Manchester United's past three matches.
The 30-year-old said there was "no embarrassment" in being on the bench.
Rooney will retain the captaincy but Liverpool midfielder Jordan Henderson will be the on-field skipper on Tuesday.
England's record scorer and most-capped male outfield player, with 53 goals in 117 appearances, Rooney has netted once in 12 games for club and country this season.
"My game now? Of course, I'm not denying it is in a difficult period. I've been on the bench the last few games for Manchester United but that's part of football," said Rooney.
"I have to work hard and, when I'm needed for both club and country, I'll make sure I'm ready."
Tottenham's Eric Dier will replace Rooney in midfield against Slovenia.
Southgate added: "We have looked at the way Slovenia play and I knew in my mind the profile of the midfield I wanted to play in this game. In no way is it a reflection of Wayne's performance on Saturday.
"He had a lot of the ball and played with great tactical discipline. It's not an easy decision to take because of the respect I have for him as the captain of this team."
Rooney said being dropped by England had not changed his plans to retire from international football after the 2018 World Cup in Russia.
"My game now? Of course, I'm not denying it is in a difficult period. I've been on the bench the last few games for Manchester United but that's part of football," said Rooney.
"I have to work hard and, when I'm needed for both club and country, I'll make sure I'm ready."
Tottenham's Eric Dier will replace Rooney in midfield against Slovenia.
Southgate added: "We have looked at the way Slovenia play and I knew in my mind the profile of the midfield I wanted to play in this game. In no way is it a reflection of Wayne's performance on Saturday.
"He had a lot of the ball and played with great tactical discipline. It's not an easy decision to take because of the respect I have for him as the captain of this team."
Rooney said being dropped by England had not changed his plans to retire from international football after the 2018 World Cup in Russia.
