Published Sunday, 18 October 2009
The article, published in Friday's Daily Mail, also prompted more than 1,000 complaints to the Press Complaints Commission (PCC).
A Metropolitan Police spokesman said: "We have received a complaint from a member of the public."
The development came after Gately's Boyzone bandmates led the mourning at his funeral in Dublin on Saturday.
Ronan Keating sang and carried the 33-year-old's coffin along with Keith Duffy, Mikey Graham and Shane Lynch during the ceremony, which was watched by thousands of people.
Gately died the previous Saturday in his apartment in Port Andratx, Majorca.
In the column about the gay singer's death, Moir wrote: "Healthy and fit 33-year-old men do not just climb into their pyjamas and go to sleep on the sofa, never to wake up again. Whatever the cause of death is, it is not, by any yardstick, a natural one."
And she signed off: "For once again, under the carapace of glittering, hedonistic celebrity, the ooze of a very different and more dangerous lifestyle has seeped out for all to see."
Moir defended her opinion piece, which ignited a huge debate on networking sites such as Twitter.
She issued a response in which she branded suggestions of homophobia as "mischievous" and claimed the backlash was a "heavily orchestrated internet campaign".
Stephen Fry was among those using his Twitter feed to mobilise opinion about the article.
At one stage he wrote: "The Press Complaints Commission website is down. Sheer volume of traffic. That says something about the strength of feeling I think."
A spokesman for the PCC said of the 1,000 complaints received, many were relating to questions of accuracy, intrusion and discrimination.
He said the PCC had already established links with Gately's family in case they had wanted to express an opinion about the coverage of his death.
Moir questioned how many of those who had complained had read her column.
She said: "Some people, particularly in the gay community, have been upset by my article about the sad death of Boyzone member Stephen Gately. This was never my intention. Stephen, as I pointed out in the article, was a charming and sweet man who entertained millions.
"However, the point of my column - which, I wonder how many of the people complaining have fully read - was to suggest that, in my honest opinion, his death raises many unanswered questions."
The newspaper said it had withdrawn online adverts that appeared alongside her article, "of its own volition" after advertisers' telephone numbers were published "by the heavily orchestrated campaign" attacking the column.