No, a blue whale is not a producer. It is a consumer.
Producers create their own food through photosynthesis, using sunlight, water, and carbon dioxide. Blue whales are animals that eat krill, which are primary consumers. Krill, in turn, eat phytoplankton, which are producers.
So, while blue whales do not make their own food, they depend on organisms that do, placing them in a food chain that begins with producers.