HMS Hermes was sunk in 1914 by a German submarine in the Dover Strait, with the loss of 44 lives.
A 56-year-old man, from Winchelsea, in East Sussex, and a 55-year-old from Teynham, in Kent, were arrested on suspicion of theft.
Items believed to be from the ship were found during the arrests, police said.
The Kent Police investigation was carried out alongside the Maritime and Coastguard Agency, the Marine Management Organisation, the Receiver of Wreck, Sussex Police, Historic England and the French authorities.
PC Preston Frost of Kent Police said: 'We are proud of our close working relationship with our partner agencies and take a robust approach to ensuring important historical artefacts do not end up in the hands of people who are not entitled to them."
Two men have been arrested following reports "historic artefacts" were stolen from a sunken Royal Navy warship in the English Channel.