Ronaldinho was jeered off the pitch when he was substituted on Saturday after his mistake had led to Internacional's equaliser in a 3-3 draw.
He was given permission to visit his mother, who has health problems, after the game but missed training on Wednesday and did not catch the flight to Teresina for Thursday's friendly.
"I've just spoken to the club president and he's been suspended," Coutinho said in a conversation which was filmed by one of the fans.
"I thought that he might not have come because of his mother's problem, but he didn't even answer the phone or call."
"Who do you think is going to win?" he added. Flamengo has existed for 100 years."
Ronaldinho's performances have been disappointing and he was left out of the Brazil squad this month by coach Mano Menezes for a tour to Europe and the United States.
