Having won their first ever Davis Cup title in November against Croatia, Argentina have a weakened team going into the tie against contenders Italy.
After returning triumphantly from injury last year, world number 38 Del Potro, 28, is skipping this year's Davis Cup to concentrate on preparing for the tour circuit.
The holders will also be without the other star of last year's title, world number 49 Federico Delbonis.
Their countryman Diego Schwartzman meanwhile will miss the first day of the tie on the clay at Buenos Aires' Parque Sarmiento due to a foot injury.
Friday's rubbers will start with Argentina's Guido Pella against Italy's Paolo Lorenzi.
Carlos Berlocq will then stand in for Schwartzman against Fabio Fognini.
The remaining rubbers were to be confirmed depending partly on the recovery of Schwartzman, world number 53 at age 24.
Team captain Daniel Orsanic could not confirm whether Schwartzman would be able to partner with Leonardo Mayer (world number 146) in the doubles on Saturday against Simone Bolelli and Andreas Seppi.
Orsanic told reporters he hoped Schwartzman would recover in time to play a singles game on Sunday.
"We are slight favourites," said Italy team captain Corrado Barazzutti.
"But we will be facing players who are very good and when they play for Argentina, they play with their hearts."
The winner of this weekend's tie will face Belgium or Germany in the quarterfinals in April.
