In US usage, there is no direct equivalent. You will find some people who use "bon appétit" occasionally. Also, someone might say "Enjoy your meal!". But I don't think either salutation is typical.
On the other hand, it would be fairly typical to ask, prior to eating "Are you hungry?", or, less commonly, "Got an appetite?". It would also be typical to ask, shortly after the start of a meal "How is the food?", or any number of variations on that theme.
Edit: it later occurred to me, as others had posted notes about both pre-meal prayers and the social and cultural intent of the phrasing in question, that US English, did, at one time, have a similar practice. Prior to the 1960's or 70's, a pre-meal prayer ("saying grace") was a prevalent practice. With the aging of the "baby-boom" generation, that practice fell out of favor. "Grace" was typically something short, and semi-formulaic. Thus, it was not something that would be directly parallel to “bon appétit” or “smakelijk”. However, if one considers the cultural intent more than the literal usage, one can find parallels. 1) It was a practice that "started" the meal. 2) It typically connoted a message of thanks, to the host, to the guests, to the sources of the food that made the meal, etc. 3) It often referred, in cultural context, to a hope that the consumers enjoy the meal. Obviously, “bon appétit” or “smakelijk” are linguistically and culturally much simpler than "saying grace", but under that simplicity is a cultural message that is inferred by their use.