This is an interesting question to me.
I actually hadn't known about what this exactly means until you asked.
Now, kindly take a look at this page.
The page says, ( though they are almost at the extinction level )
メダカ is a freshwater fish as small as 4cm and considered to be the smallest fish among them in Japan. In past times, they were found so often in rice fileds and creesk, ponds and were familiar to ordinary Japanese but the change of the environment reduced their numbers largely.
So, even though I have never heard personally the "joke" in your question for my long wasting lifetime, haha, but I think the implication of the sentence is referring to "small kid".