The British team, led by Laura Robson and Heather Watson, gained promotion from the 16-nation Europe/Africa Zone Group I in Israel last week and are now just one win away from being promoted to World Group II in 2014.
The match, scheduled for April 20-21, is likely to be held on clay with the hosts currently only having one player in the world’s top 200 in the shape of 195th ranked Paula Ormaechea after Giselle Dulko’s retirement last year.
GB captain Judy Murray said: "Argentina away on clay will be a tough challenge for us but we have a strong squad and a huge opportunity to grab a place in the World Group. Vamos!"
Argentina are facing relegation from World Group II following a painful loss to Sweden in the first round where they relinquished a 2-0 lead at the end of day one.