Fernandes was left on the bench for Sunday's 3-0 home defeat against Bournemouth after publicly questioning United's approach during their 4-1 Champions League loss to Como.
The decision raised questions about the relationship between the pair, particularly with Carrick under increasing pressure following United's disappointing run of results.
However, the United head coach has now made it clear that Fernandes remains an important part of his plans and will continue wearing the captain's armband.
The pair met at Manchester United's Carrington training ground on Tuesday, with their discussions intended to resolve any outstanding issues and allow the club to concentrate on improving its performances.
Speaking ahead of Saturday's Premier League meeting with Chelsea, Carrick dismissed suggestions that a decision needed to be made about Fernandes' captaincy.
"There's no decision to be made on that," he said.
"Listen, we are clear with the situation of the team, and as a football club, at the moment.
"He's an important player for this group. He has been and he will be.
"Between us, we've got to make a difference and we've got to push things in a good direction.
"He's fully committed to this football club, he's fully committed to making things better. There are absolutely no issues with that."
Fernandes' omission against Bournemouth attracted considerable attention, particularly after he had been critical of the team's tactical approach following the defeat in Italy.
The midfielder had questioned United's reluctance to press their opponents more aggressively, suggesting the coaching staff needed to reconsider their strategy.
Carrick subsequently insisted his decision to leave the captain out was based on footballing considerations rather than any disciplinary action.
He has maintained that position while making clear that the disagreement will not affect Fernandes' longer-term responsibilities within the squad.
"It doesn't change for me. It was a decision for what we felt for the Bournemouth game. That's it," Carrick added.
"He's the one that's led the team so well for many a game and many a year, and he'll continue to do that. There are absolutely no issues with that."
The confirmation comes at an important moment for United, with Carrick needing to restore confidence and find a way to improve results.
Their defeat against Bournemouth extended an alarming sequence without a victory, increasing scrutiny of the head coach and the club's decision to retain him in charge.
United will now travel to Stamford Bridge knowing that another disappointing performance would intensify the pressure.
Fernandes' return to the starting line-up remains a separate selection decision, although his continued involvement will be significant as Carrick attempts to bring greater stability to the team.
The manager's comments nevertheless remove one source of uncertainty, with the Portuguese international retaining the captaincy and the backing of his head coach.
For Carrick, the immediate priority is ensuring that the discussions translate into improved performances, rather than allowing the disagreement to become another distraction during an increasingly difficult campaign.