We got it for our baby at about 6 months and she has loved it. You could go a little younger, maybe as low as 4 months as we had some other books at that age, but I think she really started enjoying us reading to her around 5-6 months. It took her about 2 weeks from getting before she could move the "peek a boo" objects and looks to us in recognition of each animal. It's now one of her favorite books. She also loves the Goodnight Moon series. The book was well worth the money.
We got this for my daughter at 6 months, and she loved it! We've read it many, many times since then, and it's still brought out regularly now that she's 17 months. She loves the crinkly portions and the interactiveness of this book.
We started my daughter on this book at just 2 and a half months--right when she started focusing on things and reaching and grabbing. I say "touch" to her and she reaches and touches the owl's face on the front cover. By three months, she's able to grab all the flaps on each of the pages and pull them down when I say "touch". On the "trickier" owl page (that has to be opened sideways) she gets a good windup and swats it open. She absolutely loves this book, and I highly recommend it for babies much younger than 6 months!
My granddaughter has just turned a year old and has had this book for some time. Her mom says she loves it. The cloth pages are easy for small hands to turn (she loves turning pages) and there are flaps within the pages with pictures behind them that add to the fun. She also likes carrying books around and the cloth, vinyl or board books are the only ones with pages that don't get torn if she handles them without supervision. So that gives her a little autonomy in manipulating something independently. I would say anywhere 5-6 months on.