Library and Archives Canada hold Canadian military service records for World War 2; there will certainly be a record of your grandfather's enlistment and discharge -- armed forces the world over are extraordinarily keen on keeping records of their soldiers.
As he survived the war, his records are subject to access restrictions and not available online. The restrictions and ways of requesting a copy are here. In summary, you can apply in writing or via an online request form.
For individuals still living: Personal information cannot be released without the written consent of the individual concerned.
For individuals deceased less than 20 years: Limited personal
information will be released to an immediate family member (spouse,
parent, sibling, child or grandchild) of the individual concerned if
proof of relationship and proof of death are provided. Proof of death
is not required if the individual died while serving in the Canadian
For individuals deceased more than 20 years: Personal information will
be released on an individual deceased for more than 20 years if proof
of death is provided. Proof of death is not required if the individual
died while serving in the Canadian Armed Forces.