Murray, Britain's top-ranked men's player and No. 12 in the latest world rankings overall, dropped from the No. 9 spot after he was beaten by Frenchman Jo-Wilfried Tsonga in the first round at the Australian Open earlier this month.
He tried unsuccessfully to play through pain in his knee.
"(Medical experts) have advised me that going from hard courts to clay and back to indoor courts could increase chances of further injury," Murray said Wednesday on his personal Web site. "We had a scan done this week and have decided that it is better not to play. I'm disappointed because I love playing for my country and have always enjoyed the team atmosphere of the Davis Cup."
The British team travels to Buenos Aires for the best-of-five series of matches on an outdoor clay court to be contested Feb. 8-10.
Murray will be replaced by doubles specialist Ross Hutchins. Other team members are his brother, Jamie Murray, Alex Bogdanovich and Jamie Baker.