The 23-year-old Germany international went down six minutes after coming off the bench in Bayern's 4-2 friendly win at Heidenheim on Tuesday and required medical attention before being assisted from the pitch.
He also collapsed during Bayern's 3-1 friendly victory over RB Leipzig on Saturday.
Musiala said this week that he had been diagnosed with the disorder and that the episodes were "currently part of my everyday life".
Speaking ahead of Bayern's German Super Cup match against Borussia Dortmund on Saturday, Kompany moved to ease concerns about the player's health.
"I spoke with Jamal, he said, 'no problem, you can say it'," he told a press conference. "With his treatment, he changed some things and that had some side effects. That is normal, that during treatment you try something else."
Bayern's sporting director Max Eberl said the club were fully behind the player, who had wanted his condition to be made public.
Musiala will not be in the squad for Saturday's match, giving him time to adjust to his condition now being public knowledge.
"We've known about it the entire last season," Eberl said. "The players also knew about it. For us, it's become part of everyday life.
"He changed something in his medication, which is why these situations became clear. We will give him all our support, have already done so, and will continue to do so. We're doing this together."
Kompany said Musiala, who has struggled to rediscover his best form after a serious injury in July 2025 sidelined him for six months, had made big strides and was ready to deliver.
"I am completely calm," Kompany said. "I now expect the counter-attack from Jamal. I have the feeling that he now has all the means to deliver these answers.
"For me as a coach, I know he has taken a huge step forward."