The answer is yes.

Ontario’s Employment Standards Act, 2000 (“ESA”) provides that you and your employee can agree, in writing, that your employee will work a public holiday that they are entitled to in exchange for a substituted day off. 

If you both agree, you will pay your employee his or her regular wages or regular rate for the hours worked on Canada Day, and then you can substitute another day that would ordinarily be a working day for the employee to take off work, such as Monday June 30, 2014.  On the substituted day, you would pay your employee public holiday pay as if the substitute day were the holiday.  

An agreement to substitute a holiday for another work day is an exception to the rule that an employee be given the public holiday off.  Be sure to abide by the requirement that the agreement is in writing, otherwise you could find yourself outside of the “exception” and therefore in violation of your obligations under the ESA.