The Germany legend said Musiala showed positive signs after returning from his long-term injury, but expects the midfielder to deliver consistently now that he is back to full fitness.
"At some point, the chapter of the serious injury he suffered more than a year ago has to be closed," Matthaus told Sky Sports.
"He now needs to put it behind him once and for all. That's absolutely crucial, given the intense competition for places. He'll probably spend a lot of games on the bench."
Matthaus believes Musiala will face strong competition for a starting place, with Serge Gnabry and Lennart Karl also working towards full fitness as Bayern prepare for the new campaign.
Despite the warning, Matthaus acknowledged that Musiala made encouraging progress during the closing stages of last season and also impressed in flashes during the World Cup.
"Musiala showed promising signs toward the end of last season with Bayern, and there were encouraging moments from him at the World Cup as well. But now there are no more excuses," he said.
Musiala is expected to be fully fit for the start of the new season after undergoing a planned minor operation in July to remove a metal plate from a previous leg fracture. The procedure formed part of his recovery plan and he is now following Bayern's structured pre-season programme.
The 23-year-old is on course to be available for Bayern's opening competitive match of the season, the Franz Beckenbauer Supercup against Borussia Dortmund on August 22.
Before then, Bayern continue their preparations with a pre-season friendly against local amateur side FC Rottach-Egern on Thursday as Vincent Kompany's squad builds towards the new Bundesliga campaign.
Bayern Munich captain Manuel Neuer says the 2026-27 campaign will "very likely" be the last of his glittering career, although he insists he has no intention of treating it as a farewell tour.
Christian Eriksen's return to Wolfsburg has been delayed, with the German club making it clear that the Danish midfielder will not be rushed back as he continues his recovery.
Galatasaray have rejected speculation suggesting Jamal Musiala could be on his way from Bayern Munich, shutting down reports that emerged in Turkish media earlier this month.
RB Leipzig head coach Martin Demichelis has spoken for the first time about the transfer saga surrounding Ivory Coast winger Yan Diomande.
