Agassi, 35, sustained the injury last October forcing his withdrawal from the season-ending Masters Cup in Shanghai in November.
He has also withdrawn from the invitational tournament at Kooyong, the week before the Australian Open begins on Jan 16.
"I attempted to play in Shanghai with an injury that was not fully healed, and it set me back substantially," Agassi said in the statement. "I made a commitment to myself not to play unless I can be at my absolute best.
"Unfortunately, even with the amount of training and rehabilitation I've been going through, my ankle is still not 100 percent.
"These two tournaments mean a great deal to me.
"I'm disappointed that I will not be able to start the season in Melbourne, but I plan to return to the court as soon as my ankle is fully recovered."
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