Mash strawberries using a fork or potato masher. (If using frozen strawberries, partially thaw before mashing.)
Combine strawberries and yogurt in a mixing bowl. Mix well.
Snap each graham cracker in half.
Place a well-rounded tablespoon of the strawberry mixture on one cracker. Place another cracker on top to create a sandwich. Repeat to make 12 sandwiches.
Wrap each in plastic wrap, waxed paper, or a sandwich bag.
Put wrapped sandwiches on a flat surface in the freezer. Freeze for 2 to 4 hours.