Horner's position at the Milton Keynes-based squad was thrown into doubt earlier this year in the wake of complaints about his behaviour made by a female employee.
The probe triggered a lengthy investigation which eventually cleared Horner but triggered an internal power battle that risked tearing the team apart.
There was talk that the Thai majority owners of the Red Bull energy drinks company were fully supportive of Horner, while the Austrian side of the business, led by Mintzlaff, wanted him replaced.
This view was further fuelled by the fact that Mintzlaff kept a low profile amid the tense situation and gave no formal support for Horner despite having had the opportunity to do so during a visit to the Saudi Arabian Grand Prix.
But in a rare interview with Bild Am Sonntag, Mintzlaff has made clear that he is fully supportive of Horner and believes he can continue to lead the team to success over the long term.
"I am convinced of that," said Mintzlaff. "He only has the team's success in mind and is a very good CEO."
Red Bull's task to keep winning in the future has not been made any easier by the departure of its chief technical officer Adrian Newey, who will be leaving at the start of next year.
And while Mintzlaff is not delighted at losing someone as talented as Newey, he says the technical structure in place is one that will allow the team to continue producing great cars.
"Adrian has done great things here over the years and played a big part in us winning 13 world championship titles," he said.
"It's obviously a shame that he's leaving us, but we discussed it in a very fair and respectful dialogue. What he leaves behind is not only a unique legacy but also a structure that he helped to build.
"Of course, we will miss him – also as a person – but tomorrow we will still know how to build a very fast Formula 1 car."
The timing of Newey's departure means Red Bull will be without him for the transition into F1's new rules era from 2026, when the team will also be running its own engine.
And while not underestimating the scale of the challenge ahead, Mintzlaff sees no reason why Red Bull cannot do well with the next generation of cars.
"In 2026 we want to continue where we are currently: at the top of Formula 1," he said.
"Of course, there is no guarantee of this, but while we have proven that we can handle major rule changes, other teams have not managed to close the gap for three years.
"Max [Verstappen] will also have noticed this, and it makes me look totally positive into the future. We haven't just been preparing for 2026 since yesterday.
"Sure, building your own engine is a big task and challenge, but we are confident that we can master this step. This is the next stage of development for Red Bull."
