Spinnaker was rescued from a fishing net off the coast of Japan in 1991 and spent a decade being rehabilitated before arriving at the aquarium at about age 14.
The dolphin was under close observation by the aquarium's veterinarian for several months and had appeared to be doing well in recent weeks.
A necropsy was expected to be conducted Thursday.
In January, the aquarium's beloved sea otter Milo died at age 12.
Tiqa, a three-year-old beluga whale, passed away in September 2011 and was the third calf to die at the aquarium since 2005.