Van Dijk was sent off in the 1-1 draw away to Hungary on Friday and is banned for the next Nations League fixture.
The defender initially said that, despite the suspension, he wanted to stay with the squad to support his teammates.
"I'll just travel with the team, of course," he told NOS television following the match.
"At least, that's natural for me. I just played 80 minutes tonight, so I will first have to recover and I just want to be with the team as captain."
However, Van Dijk later changed his mind and on Saturday was heading back to Liverpool, who face Chelsea, RB Leipzig, Arsenal and Brighton & Hove Albion (twice) over the next three weeks.
"I would have liked to continue supporting the team, but I decided that I would like to go home.
"There has been a lot of talk about all the matches we have to play, all those trips. It is a good time to get some rest," he added.
Van Dijk is the first Netherlands captain to be sent off in a full international and misses an international for the first time since June 2022. He has 77 caps.
The KNVB said no replacement would be called up to the squad, which travelled to Munich from Budapest on Saturday.
