The 23-year-old, who will join Juventus once the 2019-20 season is over, didn't turn up for practice on July 27 after a week off. It's understood that Arthur decided to stay in his native Brazil and remains there today.
Miralem Pjanic will move from Juventus to Barcelona at the end of the campaign as part of a separate deal.
"It is his decision. No one has given him permission," Bartomeu added. "I assume what has happened is that he has gone to Brazil and wants to extend his holidays. That has forced us to open disciplinary proceedings against him because he has to play with Barca until the season is completed. In this case in the Champions League, just like Pjanic.
"It was an agreement between the clubs. What he has done is a lack of respect to his teammates because the team wants to do well in the Champions League and also to the club. It is unjustifiable and totally incomprehensible."
Barcelona face Napoli Aug. 8 in the second leg of their Champions League last-16 clash. The first meeting was held in February and ended 1-1.
Bartomeu is surprised Arthur would effectively rule himself out of Europe's flagship competition. The midfielder last appeared for Barcelona in a 2-2 league draw at Celta Vigo on June 27.
"Apart from the fact that if a worker doesn't work, he doesn't get paid, it's not logical that playing for such an important trophy, a player decides to erase himself (from the team)," Bartomeu said.