Griffiths has been a success for both club and country over recent years, but has had a tricky start to the season.
Despite being able to score five goals already this term, he faces stiff competition with his club from Odsonne Edouard and decided it would be best for his season going forward to not participate in the Scotland squad for the games against Portugal and Israel.
"It's brave of the wee man to do that because he wants to work on his fitness, he wants to come in here, he wants to do better," said Brown.
"Maybe going away with Scotland he's not going to get the game time that he was going to expect and the training wouldn't be as hard because of the two games coming up.
"I think Scotland and Celtic need him to be as fit as he possibly can be for the whole season and he's probably done the best thing for him to be as sharp as possible.
"As soon as he is, he's the best striker in Scotland by far. He scores goals and that's why he keeps playing in the team, but he just needs that little bit of break."