Holly Scherer of the University of Michigan Health System in Ann Arbor says fruits and vegetables that are in-season are typically priced reasonably. Buying produce by the bag instead of individually also tends to be cheaper.

"By planning ahead, shopping the sales and trying out those generic or store brands, you really can save a significant amount of money while also providing healthy, well-balanced food for your family," Scorer says in a statement.

However, buying protein on a budget can be tricky. Scherer advises saving money by buying less-prepared items.

"Season and marinate your own meat; you don't need the store to do that for you, replace meat with a protein substitute a couple times a week," she says. "You can pay sometimes three times more per ounce for meat rather than buying a substitute such as beans, eggs or peanut butter."

Buying less-processed grains in bulk is another way to save. Scherer recommends plain brown rice instead of boxed rice mixes and big containers of quick-cooking oats instead of individual packets of instant oatmeal.