Elmer's Carpenter's wood glue & a couple of clamps or heavy books placed on it until it is dry (several hours) will do it. That is glue my DH used in all the cabinets he built tho this sounds like inexpensive panel(he only used real wood) some panels are paper covered so be sure no glue gets on the front of it. You will have to take the drawer out, be sure of how it is to be positioned & then prop it up on couple of books if it has a rail & stop that sticks out the back. Glue on the piece when you have it even & clamp or use weight of books to dry. Don't get lot of glue at edges, use a cheap brush or Q-tip to put thin layer around outer area & more 1/2 in. or so toward center, should not be real thick, Carpenter's glue has good holding power. It's available at home improvement stores & hardware stores. It comes in a pint size & maybe smaller. Lasts a long time & works for many things around the house, broken piece of mop board can be glued back on if too small to nail & use masking tape to hold it firmly on for couple of days until dried. Works well to reglue loose veneer also! May need to use thin piece of wood or even toothpick to get glue under loose area, press down, wipe excess away & use something heavy to weight it down until dry.

The panel is a dwr. front and is placed as a continuation of the aesthetics of the upper dwr. line across the sink cabinet as opposed to a blank.
Its common to have a couple of cleats attached across the opening and this panel then nailed to the cleats before the sink is installed.
Attaching it with screws is a better method.
Because the reveal of the panel may be narrower than the 3/4" depth of the face frame you may have to add some filler material to the cleats before glue and clamps will affect a repair.