The bizarre stunt was caught on security CCTV in Chelyabinsk, southern Russia, as the couple created the 100-foot-long manhood by walking through the snow.
Their perfectly coordinated movements show, police believe, that they had planned the slur on the tribute to police officers who had died in the line of duty.
Infuriated officers quickly tracked down and arrested the pair, both aged 19, who have not been named.
A second video later recorded by police in front of the monument on 26th October shows the shamefaced pair confessing and apologising.
The girl says: “Dear residents of Chelyabinsk, as well as mothers and relatives of those killed in the police line of duty, we offer our deepest apologies for what we did.”
And her partner claims: “We didn’t know about the location of the monument here. We repent of what we did, it won’t happen again.”
Despite their apologies, the couple are likely to face criminal charges.
Local media reports that it is hard to believe the couple did not know what they were doing.
The monument has a 50-foot-high bronze statue of a police officer standing with his head bowed beside a small boy looking up at him.
Flanking them are six giant tablets carved with the names of 232 police heroes who have died in the line of duty since 1918.
A regional police spokesperson said: “With their actions, the unknown persons insulted not only the bright memory of the employees who died in the line of duty, who gave their lives for the well-being of the people of the South Urals and who fell in the fight against crime, but also all the Chelyabinsk residents who were grateful to their exploits.”
They added: “Finding the identities of the young people who committed the blasphemous act and then bringing them to justice became a matter of honour for the police.
“The most experienced criminal investigation operatives of the Chelyabinsk Department of the Ministry of Internal Affairs and local police officers joined the work.
“The police interviewed a large number of possible eyewitnesses and found out the route of movement of the violators.
“Having carried out the most complex, painstaking and persistent work, operatives and local police officers identified and detained the wanted persons.”