It carries a crew of over 200 naval cadets, according to Russian state media.
The ship has just taken part in a biennial, multi-lateral naval exercise in Indonesia.
The PNG port call is the latest in a series of Russian military-related forays to the Pacific region in the past couple of years.
Last December, Russian strategic bombers conducted navigation exercises in the western Pacific, flying out of an Indonesian military base in Papua.
The five-day stopover put Australian military forces in Darwin on high alert.
In 2016, Russia sent twenty containers of weapons and military hardware to Fiji, stationing Russian troops there for a period for reported training purposes.
The two governments said the hardware and training were to help Fiji in its peacekeeping missions overseas.
PNG's Foreign Minister Rimbink Pato has described the Russian warship's stop in Moresby as a goodwill visit related to his country hosting APEC meetings this year.
According to a media release from Mr Pato, at a meeting of APEC officials from various member economies this month, PNG arranged to host a crew of cadets learning about naval traditions and practices.
According to the minister, while in PNG the cadets would learn about local culture and customs. He said the visit was the first of a range of visits by APEC members in the lead up to the APEC Leader's Summit in PNG this coming November.
"We welcome youth from all APEC member economies prior to - and during - this great event for our country," Minister Pato said.
"This is not a formal port visit by the Russian Navy but rather a goodwill visit for young people, arranged at a convenient time with so many able to come to our country at once."
"Naturally, we have informed the Australians, our major security partner and close neighbour, and advised them of the nature of the visit.
"As is usual with our friends and ally, the Australians welcome our attempts to draw attention to the forthcoming APEC summit, and they support our efforts to cultivate friendship and understanding among the youth of APEC nations."