The man and woman were bitten as they fled following a suspected car theft in the Vancouver Island city last Saturday morning.
Police say the woman was treated and released but the man was more seriously hurt.
An IIO team was on the scene within hours and has completed its preliminary investigation.
The office has now released a statement saying while the incident was officer-related, the victims' injuries do not meet the definition of serious harm, so the IIO does not have jurisdiction.
The case has been closed.