Is replacing a damaged garage door covered under home insurance policy?

It depends on how the door was damaged. If it is normal wear and tear, no, its not covered. However, if the door was damaged by a covered loss (read the Perils Insured Aganist section of your policy) then the insurance company will cover the loss. Also you may want to see how much the replacement door will cost. If the cost of the door does not exceed your deductible then there is no sense in reporting the claim.