There's a couple ways to address this semi-systematically.
The first is to take his pre-injury projected value and then discount it for the risk of injury. So if you had him as a $40 player, reduce that by the time that he might miss (say 40% of the season) which is also discounted by the probability that it might happen (this is the tough one; I haven't seen any numbers on this). So if you knew he was going to miss 40% of the season but perform perfectly fine otherwise, he'd become a $24 player. If you think, for whatever reason, that his chance of missing time was 50% then he'd be a $32 player. Then you can slot him into your player rankings and see where he lands.
Somewhat less systematically, you can look at the players you'll be passing up and seeing who you'd rather take.
Using the MDP spreadsheet
(which uses a 12-man league):
1st-rounder: Tex is the last pick in this round. I definitely would rather have Tex than A-Rod and his injury concerns.
2nd-rounder: Prince Fielder/Manny Ramirez are the bookend 2nd/3rd round picks. I'd still like one of them over A-Rod.
3rd-rounder: Aramis Ramirez is the last pick in this round. Call me cautious, but I'd also take Aramis over Alex at this point.
4th-rounder: Now you see names like Alex Rios, Brian McCann, and Russell Martin and are close to Curtis Granderson. These are the players who have performed well but you would have a shot at replacing their production with a good sleeper pick later. Some time around now is when I would take a flier.
0-3 to 4-3. Worst choke in the history of baseball. Enough said.