The Pumas replace England, whose 28-14 loss to Australia at Twickenham has seen them drop to fifth position.
In terms of the 2011 Rugby World Cup draw on December 1, which will use the rankings to seed the 12 pre-qualified teams, Argentina now occupy one of the top four positions.
If they remain there, the Pumas would avoid being in the same World Cup pool as the top three teams - currently New Zealand, South Africa and Australia.
So for both Ireland and Argentina, there will be a lot more than just bragging rights on the line and scores to settle when the sides clash at Croke Park (kick-off 2.45pm) next Saturday.
In order to get a more favourable World Cup draw, Ireland need to beat Argentina to remain in the top eight of the rankings.
Ireland did not lose any rankings points despite their 22-3 defeat against New Zealand, as the rating gap between the two teams was too big.
But Declan Kidney's men know that defeat to Argentina next weekend, combined with a Scotland win over Canada, would see them drop to ninth in the rankings and into the third band of teams for the World Cup draw.
Crucially in that scenario, Scotland would move up to eighth and into the second band for the draw.
Kidney said: "We have a huge, huge game next weekend. Trying to get into the top eight is in our own hands. We've to try an beat a them thats ranked above us and we haven't done that for a while.
"We'll pick ourselves up and get on for this next game. There's no hanging around (feeling disappointed about the New Zealand game)."
IRB WORLD RANKINGS (As of Monday, November 17, 2008):
- Last week's position in brackets
1(1) NEW ZEALAND 92.41 rating points
2(2) SOUTH AFRICA 88.45
3(3) AUSTRALIA 86.70
4(5) ARGENTINA 82.82
5(4) ENGLAND 82.11
6(6) FRANCE 80.13
7(7) WALES 79.58
8(8) IRELAND 77.18
9(9) SCOTLAND 76.76
10(11) FIJI 75.24