The 23-year-old takes the place of Tom Lineham, who injured an ankle in his side's 38-20 derby victory at Craven Park last Sunday and is given only an "outside chance" of facing Wigan in the Tetley's Challenge Cup final on Saturday week.
Crookes' call-up comes just 24 hours after he was convicted by Hull magistrates of assaulting two women at a city-centre bar last December.
He was given a 12-month conditional discharge but has received the full backing of his club.
"We feel the player has been harshly dealt with and we stand by him," Hull owner Adam Pearson told the Hull Daily Mail. "We all make mistakes and Jason has paid for his. We all now move on and the player has our full support."
Hull coach Peter Gentle told a news conference at the club's training ground that Crookes had already put the court case behind him and fully deserved his opportunity in the team.
"He's fine," Gentle said. "He's been waiting a while, he's very popular within the group. The boys are disappointed with what's happened to Tom but you couldn't hide the excitement on Jason's face in training. He's got a great opportunity."
Crookes has made just nine appearances since joining Hull from Bradford in the close season.
Lineham, who has scored 17 tries in his first full season, has not yet been ruled out of the cup final but looks certain to join centre Ben Crooks and full-back Shannon McDonnell on the sidelines as Hull go in search of their first Wembley victory.
"We still don't know the full extent of the injury," Gentle said. "We haven't ruled him out of next week's game just yet. He'll get an opportunity to maybe prove his fitness one way or the other next week. He's an outside chance and, while there is that, we're willing to give him as long as it takes."
Hull will be without experienced Australian prop Mark O'Meley for the visit of Salford with a slight leg strain but hope he will be fit to face Wigan. Former captain Andy Lynch returns to take his place after missing Sunday's game with a minor leg injury.
There is no place in the squad for long-serving utility back Richard Horne, who is close to completing his recovery from a long-standing foot injury and has not yet been ruled out of the cup final.
Horne, who is one of two survivors from Hull's final appearances in 2005 and 2008, has missed the last 10 matches but Gentle insists he would have no qualms about bringing him straight into the side for Wembley.
"He's played a lot of footie, he doesn't really need a game under his belt to go into it, even though it is a cup final," he said. "He's been around the park enough to know his way around. It doesn't concern me.
"He could have probably pushed it to play this week but, rather than take the risk of him breaking down, we'll make a decision next week on him."
Gentle admits Horne could come into the reckoning for the full-back berth against Wigan, along with Jamie Shaul, who has played the role in the last two matches, and the versatile Richard Whiting, who stepped into the breach early in the semi-final against Warrington when McDonnell damaged a hamstring.
"We've a few options there," Gentle added. "There are a couple of ways we can do things but I don't want to talk about selection until we get past Salford."