Traffic tickets are not reported directly to insurance companies. Moving violations are placed on your driving record and then your insurance company finds out about them when they pull your motor vehicle record (MVR) or when they request violation information from you on an application or questionnaire.
Maryland and the District of Columbia are both members of the Drivers License Compact so moving violations information is typically passed between the states so that the state which licensed the driver who committed a traffic violation is notified of an out of state offense.
The Maryland Driver's Handbook states that convictions reported from member states are treated in the same manner as if the offenses occurred in Maryland. Convictions for moving violations received from other jurisdictions are recorded on the Maryland driving record.
Maryland also has red light cameras that allow for photos to be taken of those entering an intersection after the light has turned red and thus sends them a citation. However, according to the Maryland District Courts site, payment of the penalty for this type of violation does not result in MD points being assessed to your driving record and cannot be used to increase your insurance rates. It is basically handled as a parking ticket.
Since the MD handbook states that the MD Motor Vehicle Administration (MVA) handles out of state violations as if they occurred in state, we deduce that the Washington, D.C. red light camera offense should also not be assigned points or affect your insurance premiums. To make certain this is true you may want to check with the MVA.
As for needing to report this to your insurance company, the Maryland Insurance Administration could tell you for certain if need to tell your insurance company about this DC ticket, even though it is not suppose to affect your rates.