An army bomb disposal team has now been called to Sandsend after the discovery was made at around 2pm on Tuesday.
An 100-metre cordon has been put in place by the Coastguard and parking has been suspended nearby.
The beach is currently closed to the public from the steps at Sandsend to the entrance to Raithwaite Hall.
Adam Turner, senior coastguard operations officer for UK Coastguard said:
"We won't know exactly what we are dealing with until the Explosives Ordnance Disposal team arrive. Until that time, we have taken measures to set up a cordon and clear that area of the beach to keep the public safe. We are appealing to people to stay from this area until it has been declared safe by the disposal team. "We have no further information at this time but we will hopefully provide an update after the ordnance team have assessed the situation."
The town of Whitby was shelled by two German battlecruisers during a World War One raid on the Yorkshire coast in December 1914. The ships aimed at a signal post, but hit Whitby Abbey during the attack before escaping.