Bellamy will remain as the Storm coach for the foreseeable future after the NRL club revealed on Thursday night that the 66-year-old had been diagnosed with the disorder following recent testing.
Stuart and Bellamy are two of the NRL's closest coaches, having played for the Raiders in the late 1980s and early 1990s, including the 1990 NSWRL grand final win over Penrith.
Their friendship has continued to the present day, with the pair catching up most recently when the Raiders beat the Storm 26-22 on April 17.
Before their round-seven clash, Stuart declared that Bellamy is the best coach in the modern era and that he holds him in high regard.
When asked whether he was aware of his friend's situation, Stuart said he knew about Bellamy's condition about three or four weeks ago.
"I know he's getting very good advice (and) got good people around him ... in Melbourne," Stuart said on Friday.
"He's got a beautiful family, so it's now time for Craig to really care about Craig and put himself first."
In February, Bellamy signed a contract with the Storm until the end of 2028 and the club is backing him to continue through the current season.
In a statement Melbourne said it had been "advised by specialists that his diagnosis will not have an impact on his ability to coach the team in the immediate future".
Taking over at the Storm in 2003, the 66-year-old has coached 614 NRL games and boasts a win rate of almost 70 per cent, while he also played 150 matches for Canberra.
Parramatta mentor Jason Ryles says he found out about Bellamy's news on Friday morning, having been an assistant coach under him between 2016 and 2020 before returning to Melbourne for the 2024 season.
Ryles was touted as a candidate to assume Bellamy's role before he re-signed, and the Eels coach said that his learnings from starting his coaching career beside the Storm mentor help him now.
"He (Bellamy) makes a grand final every two years, and he's done it for 20 years, and I don't think that will ever be replicated again. That speaks to him and his legacy in our game," Ryles said.
"He's an incredibly successful coach, and you don't do that by not being a good person."
Brisbane coach Michael Maguire, another former Raiders teammate and a Storm assistant under Bellamy for five years, said the veteran was a "fighter".
"Craig and I have had some great times together and you obviously care about the people who have been a part of your career," Maguire said on Friday.
"Knowing Craig I know he'll be right, he's a fighter and he'll get through this and keep coaching."