The 29-year-old was attacked in the Meenan Square area of the Bogside at around 8.30pm on Tuesday.
A PSNI spokesperson described the shooting as "a punishment style attack".
SDLP MLA Pat Ramsey has spoken out against those who carried out the shooting.
"I have spoken to the man's family and thankfully his injuries are not-life threatening.
"The people responsible for this cowardly attack have absolutely nothing to offer the community," he said.
"Enough is enough; people do not want to see any individuals dragging us back to the dark days of the past. I would appeal to people to think about what message they are sending out to the rest of the world when they engage in such thuggish and brutal behaviour."
Police appealed for anyone with information to contact them.