A controversial question because to fully understand the answer you need to know about the keiretsu structure and how it changed both prior to and after World War II.
But the basic answer is, no, Nikon is an independent company with its shares publicly traded on the Nikkei.
In Japan there is a history of "company groups", or keiretsu. A keiretsu is basically an affiliation of complementary companies, usually with interlocking business relationships and share holdings, For example, former Mitsubishi-owned companies, in particular what is now Bank of Tokyo-Mitsubishi, hold a percentage of the outstanding shares in Nikon (<5% the last time I looked).
In recent years the lines behind keiretsu have blurred, mostly due to bank mergers between formerly keiretsu-specific financial institutions. Moreover, the old strong alliances amongst companies have mostly broken down into more informal relationships, though major companies in a keiretsu meet regularly behind the scenes to discuss and coordinate mutual interests. That would include Nikon meeting in the Mitsubishi keiretsu.
Nikon buys components from companies in different keiretsu, as do Canon and others. Sony and Panasonic have risen in size to essentially become their own unique entities now, and are not really in a formal keiretsu system any more. Nevertheless, money talks. Much of what used to be keiretsu influence is now banking influence. Mergers between Japanese banks have produced some interesting side results, where they suddenly find that they're highly invested in multiple competing companies. Some theorize that the sales of Pentax (to Hoya) and Konica/Minolta (to Sony) were partially triggered by banks trying to rationalize their investment portfolios after mergers.