I don’t think so!
Kierkegaard spoke of nihilism:
Søren Kierkegaard (1813–1855): The nineteenth century Danish theologian Søren Kierkegaard—who many academics regard among the first existentialist philosophers—wrote about nihilism, calling it “leveling.” Kierkegaard felt that leveling was not a positive thing, because the problem of nihilism was that it meant everything was meaningless and it suppressed individuality. He felt that human life did have intrinsic meaning and therefore believed a person should avoid nihilism at all costs. link
Are you perhaps equating postmodernism to nihilism and because you see a bit of postmodernism in Kierkegaard you are thinking of him as nihilist? But postmodernism is far far too broad of a thing (naming an entire era) to equate with nihilism!