The Royal Regiment of Scotland soldiers reportedly became embroiled in a row after travelling to Manhattan to play in a rugby match against the NYPD.
Police said three or four men lashed out in the early hours of Friday morning when the officer started chatting to a woman who was with the troops.
One soldier is accused of grabbing the policeman's mobile phone and a chain around his neck when he attempted to call 911.
The soldiers - Iosefo Yavala, Iliakini Raderua, Thomas Shute, Felite Vunisarati, Mosese Kuruala and Joeli Raduva - were arrested when police arrived at the scene at around 4.40am on Friday (9.40am BST).
Yavala was charged with robbery and assault following the fight outside the Mercury Bar in the Murray Hill area of Manhattan.
The other five were each charged with a single count of assault.
The six soldiers - members of the regimental rugby team - were due to play at the Mystic River Rugby Club in Boston yesterday. Raduva is a Territorial Army lance corporal who was mentioned in dispatches in 2011, according to reports.
They could face discharge if they are found to have breached the Army's strict code of conduct.
An NYPD spokesman said: "On Friday 30th at 4.40am (9.40am BST) in front of Mercury Bar, 493 3rd Avenue, an off-duty officer was punched and robbed by three or four males.
"The off-duty officer called 911 and officers responded. Six arrests were made in regards to the incident."
The Ministry of Defence said any soldier who fails to meet Army standards may face disciplinary proceedings.
A spokesman said: "We are aware of an incident in New York involving some British soldiers.
"This is a matter for the NYPD and it would be inappropriate to comment while there is an ongoing investigation.
"All those who are found to fall short of the Army's high standards will face disciplinary action, up to and including discharge, if appropriate."