Belgium coach Domenico Tedesco said the Real Madrid goalkeeper abruptly left camp after he did not feel respected within the team, but Courtois denied Tedesco's claims and said he left the camp due to a knee problem.
Courtois, 31, played in Saturday's 1-1 home draw with Austria, but told Tedesco after the match that he would not make himself available for Tuesday's game in Estonia.
"Together we decided that Romelu would be captain against Austria and Thibaut tomorrow against Estonia," Tedesco told reporters on Monday.
"That was okay for everyone, but after the match he [Courtois] suddenly wanted to talk to me and said he was going home because he was disappointed and felt offended.
"From the beginning I tried to show him the appreciation he deserves. In my eyes he is the best goalkeeper in the world. I love him as a goalkeeper but also as a human being. I am shocked."
In a statement, Courtois said he's "deeply disappointed" with the situation and Tedesco's "assessments do not fit with reality."
"This is not the first time or the last time that I talk to a coach about issues related to a locker room, but it is the first time that someone decides to tell it publicly," Courtois said.
"I am deeply disappointed with this, but I want to make clear that the coach's assessments do not fit with reality.
"I have not demanded anything and I have spoken to my teammate Romelu Lukaku to clarify any circumstances related to this situation."
Courtois added he underwent a check-up on Sunday for "a problem in my right knee" and after a consultation with Real Madrid and Belgium medical teams, he decided to exit the training camp.
Tedesco, who took over the coaching reins from Roberto Martinez after a surprise first-round exit at the World Cup in Qatar last November, would not be drawn on Courtois' future with the national team.
"It's not the right time to say anything about that, because we have an important game tomorrow," he said. "The next games are in September and we will see then."
Courtois has earned 102 caps since making his Belgium debut in 2011, while Tedesco confirmed Matz Sels would start in goal against Estonia and add to his two international appearances.
Belgium have four points from their opening two qualifiers in Group F, having also won 3-0 away in Sweden.
The Associated Press and Reuters contributed to this report.