The American teenager incurred the wrath of his manager on Saturday when he was late reporting for duty ahead of a 0-0 draw with Portsmouth.
Altidore was subsequently removed from the Tigers squad for failing to turn up on time and was fined two weeks' wages.
He later issued a public apology, but that did little to defuse Brown.
The Hull chief has, however, had time to reflect on the incident and admits he is prepared to give the on-loan forward a second chance to prove himself.
"He'll be back in contention for the weekend (against Burnley) but it's up to him now to prove that he's deserving of a place," Brown told the Hull Daily Mail.
"He's 19, he's at the beginning of his career but Jozy is being paid an awful lot of money to play professional football and it's part and parcel of his working life to be professional.
"The word professional to me means that you do everything right, even when people are not looking at you.
"He's apologised to his team-mates because he let them down."
LearningWhile Brown was disappointed at Altidore's actions over the weekend, he feels the youngster still has the potential to be a success in the Premier League this season.
"He's been out on the training ground doing what 19-year-old lads should be doing, learning his trade," he added.
"People might look at a double-session on a Monday and think he's getting punished, but he's had an hour-and-a-half of football and an hour working on his technique in the afternoon - that's what young footballers should be doing.
"We've got hold of a young lad with big potential but to realise that, he has to do everything he can to maximise it."