I'm sorry, but I disagree with those who tell you just to let it go. That's how you become the scapegoat. Your performance reviews will suffer, and if your boss were to suddenly leave the company, what would the higher-ups know about you? That you ignore assigned tasks? If you let this go, that's the position you're putting yourself in. You need to professionally, but quickly, nip this in the bud. A boss who throws subordinates under the bus like this is not a good manager, and likely is in trouble with his boss for more issues than this. Protect yourself.
Here's what I would do. Reply to your boss' email. Do not cc anybody else, but save the e-mail for future reference, should you ever need it. Simply say, "Bob, I'm confused by this e-mail. When we spoke, you mentioned that you were going to assign this project to Harry, and that you didn't have any details on it yet. From the content of your e-mail to the client, it sounded like I should have been working on it already. Did I miss an e-mail on this? I sincerely apologize if so. At this point, Harry and I are short on details as to how we should proceed. Specifically, we need to know X, Y and Z. Please advise! Thanks, Michelle."
This accomplishes several things. One, you haven't copied anybody, so you're not throwing HIM under the bus. Two, you are gently calling him out for throwing YOU under the bus, giving him the out of "I may have missed your e-mail on this" - which you both know didn't happen, but at least you aren't calling him a jerk to his face. Three, you are showing that you've already moved on, and just want to get this project handled ASAP for the client, no matter who dropped the ball.
My instinct is that once you allow him to throw you under the bus unchecked, it will come back to haunt you. Good bosses don't do what he did. Stand up for yourself, but be professional about it. This has worked well for me in my 15 years in the corporate world. Now I own my own business (in a male-dominated field) and I would never - NEVER - throw an employee under the bus like that. A failure by my team is a failure by me, and blaming an underling will not fool anybody. Your boss has shown he can't be trusted, so just bear that in mind and put EVERYTHING in writing going forward.