The world number two announced on Twitter that the decision had been taken for him not to feature in the opening Group B match against hosts Australia.
"Hi all, we have decided with Team Spain and my team, to not play today the first match of the ATPCup here in Melbourne since I have a stiff low back.
"Hopefully I'll be better for Thursday. We have a strong team, all the to Pablo Carreno, Roberto Bautista Agut and Marcel Granollers," he wrote.
Greece are the opponents for Spain on Thursday as players continue to prepare for the Australian Open, which gets under way next Monday.
Roger Federer is also injured and withdrew from the ATP Cup - but the remainder of the world's top 10 players are competing, including number one Novak Djokovic.
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