When a protein is folded, bonds are created and we know that when bonds form, water is lost (dehydration synthesis) and energy is released. Energy is this case refers to gibbs free energy - meaning that unfolded proteins will fold and form interactions (in the right environmental conditions - temperature, pH etc) and these folded proteins are more stable than the unfolded state - i.e folding process is spontaneous.
So, using the ∆G=∆H-T∆S law, we know that ∆G is negative and ∆S is negative - we can determine that ∆H would also have to be negative and the process will be exothermic.
Keep in mind that when you are thinking of bonds breaking (energy and water are added to break bonds) and bonds forming (energy and water being released), energy is referring to ∆G. But overall, the breaking of bonds is a spontaneous (negative ∆G) process because more energy is released when you break the bonds than the amount of energy you need to put in. For example, glycolysis.