Two Sydney beaches have closed indefinitely after a heavily decomposed whale carcass washed ashore at Lurline Bay, a rocky cove between Coogee and Maroubra in the city's eastern suburbs.

Randwick City Council imposed the swimming and surfing ban on Thursday after discovering the remains. The council has signalled no immediate plans to remove the carcass, instead prioritising what it describes as a "culturally respectful" approach to the remains.

The closure affects Maroubra and Coogee, both popular swimming and surfing beaches. The carcass remains in Lurline Bay, a location surrounded by cliffs that makes access difficult.

The level of decomposition and the council's stated intent to handle the remains with cultural sensitivity suggests the council may be consulting with Indigenous groups or applying protocols that recognise the cultural significance of marine mammals to local Aboriginal communities.

No timeline for reopening the beaches or resolving the situation has been provided in available reports.