David Ferrer, John Isner and Gael Monfils have already abandoned their places in the draw due to injury or illness, and Robredo has now joined that list.
The 32-year-old Robredo was due to face New Zealand wildcard Michael Venus in the second round, but decided he could not risk further injury ahead of next week's Australian Open.
"I have been one and a half days without practising and trying to recover to play here, but I'm not ready to play a match," he said,
"I don't think it's fair for the players and the tournament for a player to get on the court and play four or five games and as soon as I felt something, which I would for sure, to withdraw. It could make me worse for next week."
As Roberdo had been handed a bye into the second round due to his seed, Venus will now play lucky loser Lucas Pouille for a spot in the quarter-finals.