The 77m-long cargo ship, called Alta, was brought to the attention of the Irish Coast Guard around lunchtime on Sunday by a local who spotted the vessel.
It had been drifting unmanned in the Atlantic for more than a year.
"The Council is currently liaising with the Irish Coastguard in relation to the pollution risk and with the Receiver of Wreck in relation to ownership of the vessel which grounded at Ballyandreane, Ballycotton, Co. Cork today," it said in a statement.
"Cork County Council, which has responsibility for land-based oil pollution risk, is continuing to monitor this ship in relation to any possible oil spillage or risk arising from cargo.
"The Council understands that the vessel was most likely diesel-fuelled which poses less risk of pollution than heavy fuel oil.
"The exact risk level cannot be confirmed at this time. The ship will be inspected tomorrow in daylight and from a land vantage point in order to access this further.
"Cork County Council does not believe that this wreck currently poses a risk to the Special Area of Conservation within the Ballymacoda/Ballycotton area."
Speaking to The Echo, the Coast Guard said that there were no immediate plans for the vessel, which drifted a considerable distance to the Cork coast, despite having no crew on board.
The same ship was then spotted off the West Coast of Africa in September of last year, before coming to the attention of the authorities for a third and final time off the Cork coastline.