The attack on Mr Greig, who was wearing an All Blacks hat when set upon, follows last year's assault on All Blacks chairman Mike Eagle and director Gerard van Tilborg by two men who stole Mr van Tilborg's Rolex watch.
That incident, a day after the All Blacks test at La Plata, also occurred near the team's hotel in Buenos Aires, which is known as a relatively safe area.
Several New Zealand supporters were also targeted by opportunists last year and TVNZ reporter Steve Marshall had his camera stolen.
Undeterred by the experience and his painful injury, Mr Greig went to the test where he hosted business colleagues, but said he had learned a valuable lesson.
"Most people are great down here - [it's] a pity that the street criminals prey on tourists. Next time I will stick to busier streets and be more aware."
Mr Greig said the incident didn't spoil his enjoyment of the game, which the All Blacks won 33-15.
"The ABs looked good in the second half. I enjoyed the way the locals respect the haka."