Health officials are awaiting test results on a 12th child.
Over the past month, officials have tracked measles to schools, grocery stores and the Del Mar Fairgrounds.
One of the latest victims is an 8-year-old who may have spread the measles virus during a visit to Whole Foods Market in Hillcrest and later to a Cirque du Soleil performance at the fairgrounds.
Officials are warning that the highly contagious disease can be particularly dangerous to children. The virus can survive for about two hours after it is expelled by a cough or sneeze.
This is the most measles cases in the city in 17 years, according to Dr. Mark Sawyer, a pediatrician and infectious disease specialist at Rady's Children Hospital in San Diego.
The outbreak is believed to have started with a child who caught measles in Switzerland, then returned to the United States.
Sawyer told Early Show co-anchor Maggie Rodriguez measles "is probably the most contagious infectious disease that we deal with," adding, "It's a miserable experience for children to have the measles."
Measles can cause complications that can even lead to death, Sawyer warned.
None of the 11 patients had been immunized.
What does Sawyer say to parents concerned about possible links to autism and other problems with vaccinations?
"The first thing I say is they really should discuss all their concerns with their physician and get all of the facts. In my opinion, parents who choose not to have their children vaccinated are not making a fully-informed decision.
"They have to realize that these diseases are out there, and this outbreak is an example of that, and not just the measles. We had an outbreak of mumps in the United States a couple of years ago. We still see whooping cough in the United States in very large numbers.
"So, the diseases are out there, and the diseases are just a plane ride away, as also illustrated by this case. This child went to Switzerland and brought the measles back here, to San Diego.
"The other thing that parents need to know is that vaccines are very, very safe, and there is a very complete structure to evaluate the safety of vaccines both before they're given to children or put on the market and afterwards."
For more on measles, check out these Web pages:
National Center for Infectious Diseases
Centers for Disease Control and Prevention (CDC)
Measles Outbreak Information from Rady Children's Hospital