Last year's US Open champion first felt the injury in Shanghai last October and it failed to clear up going into the New Year.
The 21-year-old, world No.5 struggled through the early rounds in Melbourne before losing to Croatia's Marin Cilic in the fourth round.
He returned to South America to train, but aggravated the problem again this week and decided to take a break, sources close to the player said.
Del Potro will miss the ATP events in Marseille and Dubai and Argentina's Davis Cup tie against Sweden. He will aim to return to action at the Masters Series events in Indian Wells and Miami.