The Department of Conservation has asked people along Otago's coast to keep an eye out for the whale which has the rope wrapped around its tail fluke, body, head and also possibly its mouth.
It is trailing a long length of rope that may be attached to a craypot.
So far, no sightings have been reported.
Doc biodiversity assets programme manager David Agnew said southern right whales came close to shore to breed during the winter.
"It is likely the rope is impeding the whale's movements and it is only able to move slowly.
This means it might be seen off the Otago coast in the coming days. It is likely to be distressed at being entangled and the rope could cause it injuries."
Doc is asking people to call 0800 362-468 if they see the whale and attempts would be made to disentangle it.
