It was not the first time he had made the same mistake and manager Walter Smith has admitted it is a concern ahead of Tuesday's Champions League clash with Stuttgart.
And striker Miller has now criticised his team-mate for not sticking to the rules like everybody else.
"If you are given a time to come back, you come back. It's as simple as that," Miller told the Daily Record.
"We never have a problem like that when any of the Irish or Scottish lads are away, so I don't see why it should happen if a foreigner is playing and he qualifies for a World Cup.
"We have a job to do. Rangers pay our wages and when we are asked to come back, we've got to come back."
Bougherra is an important player for Rangers and Miller is frustrated that he has not respected his club by reporting back on time.
"It's disappointing because we all want Madjid playing in the team," Miller explained.
"There's no doubt he's one of our best players and has been a big performer for us last season and this term.
"We want him in the team so when he doesn't come back it is obviously disappointing."
Rangers v VfB Stuttgart 1st Goalscorer: Miller, K. 15/2