The phrase Grown Not Made is a tagline, a form of trademark, owned by Heinz.
In some of its incarnations, it is written Grown, Not Made. This makes clear that a contrast is being drawn between Heintz' purported natural (grown) products and highly processed or chemically enhanced (made) products, sold by others.
Taglines are often fragments and do not necessarily conform to the highest grammatical standards. However, as a sentence fragment, it seems to be fairly clear that the meaning is
[Heinz products are] grown, not made.
In that context, the phrase is internally grammatical and logical. Without the comma, the meaning and grammar are arguably a bit more ambiguous. However, as pointed out by 10b0, the phrase grown not is not standard. As such, there is little likelihood that it would be read to mean the opposite of what is intended.