The two-metre (more than six-feet) high monument, in the shape of an iPhone, was erected outside a St Petersburg college in January 2013 by a Russian group of companies called ZEFS.
Citing the need to abide by a law combating "gay propaganda", ZEFS said in a statement on Monday that the memorial had been removed on Friday -- the day after Apple CEO Cook had announced he was homosexual.
"In Russia, gay propaganda and other sexual perversions among minors are prohibited by law," ZEFS said, noting that the memorial had been "in an area of direct access for young students and scholars".
"After Apple CEO Tim Cook publicly called for sodomy, the monument was taken down to abide to the Russian federal law protecting children from information promoting denial of traditional family values."
Promoting "traditional values", President Vladimir Putin last year signed a law prohibiting the spread of "gay propaganda" among minors.
Putin says there is no discrimination against gay people in Russia and the law was needed only to protect young people, although members of the gay community say its passage has increased problems for them.
ZEFS - or West European Financial Union - groups companies offering a range of products and services in areas such as real estate, construction, advertising and microfinancing.
Cook said he had decided to come out to help move forward civil rights, confirming a fact that had been widely known in the Silicon Valley tech community but was rarely discussed.
Steve Jobs, who died in 2011, was not gay.
Vitaly Milonov, a St Petersburg legislator who has campaigned against gay rights and was among legislators behind the law signed by Putin, has called for Apple's CEO to be barred entrance to Russia, Russia media have reported.
Maxim Dolgopolov, the head of ZEFS who ordered the removal of the monument, expressed opposition to personal sanctions in Monday's statement, but supported the "protection of traditional values" by law.
"Sin should not become the norm. There is nothing to do in Russia for whose who intend to violate our laws," he said.
The "gay propaganda" law caused outrage and protests in the West, particularly in the run-up to the Winter Olympics hosted by Putin in the Black Sea resort of Sochi in February.