I have just read in "A history of Japan" by Mason and Caiger that they were introduced in Tokugawa period (~XVI aD) but this affirmation seems strange to me. Didn't they develop this technology in Ancient China before? How come such a efficient way of fishing not be introduced before? When was fishing net introduce in Europe? I guess it must be in the times of Roman Empire or even before...
They might have mistaken their sources for specific types of fishing nets, because fishing did take off in the Edo period. I'm not a specialist in this area unfortunately.
I can tell you with a quick search that we have evidence of fishing nets being used since the Jōmon period (later paleolithic and neolithic periods) and the word "net" appears in the Nihon Shoki (720 AD) and "fishing net" appear in Shoku Nihon Kōki (869 AD), so fishing nets were used in Japan literally since time immemorial.