The Argentine World Cup winner has been axed for Saturday's FA Cup quarter-final against Port Vale and next Sunday's Premier League clash with Manchester City.
Fernandez, who has been wearing the captain's armband in the absence of injured Reece James, said he would "look at his options after the World Cup" and expressed a desire to live in Spain.
"I spoke with Enzo an hour ago. As a football club, with me as part of that process, we've made a decision he won't be available for tomorrow's game (against Port Vale) and he won't be available for Manchester City next Sunday," Rosenior told reporters.
The 25-year-old midfielder, who is contracted until 2032, has been linked with a move to Real Madrid, though he denied talks with the Spanish club were taking place.
'Disappointing' leadership
Rosenior described Fernandez's public comments as "disappointing" given his leadership role during Chelsea's current problems.
The Blues have lost four consecutive games, exiting the Champions League in an 8-2 aggregate humiliation by Paris Saint-Germain and have slumped to sixth in the Premier League.
"I think for Enzo it's disappointing to speak in that way. What I will say about Enzo is that, in terms of him as a person, I've got no bad words to say," Rosenior added.
"But a line was crossed in terms of our culture and what we want to build, so we had to make a sanction."
The Telegraph reported that several Chelsea players were unimpressed by Fernandez berating his teammates on the pitch.
"The door is not closed on Enzo, that's very important. It's a sanction," Rosenior said. "You have to protect this club and culture," he said. "The line was crossed in the international break.
"What I do know is that when he's been on the pitch, even in the loss at Everton, there was no lack of commitment in his performance."