The England centre-half made just three appearances last season as he was hampered by a groin injury, and he will miss Spurs' pre-season tour of the United States to work on his own personal fitness programme.
"It's make or break for Jonathan now," Redknapp told the Daily Telegraph. "He has got to come back and play. If he is not ready for the start of the season it will be difficult for him.
"When he gets his boots on and starts playing hopefully he will be all right."
He added: "He is a fantastic player: one of the best centre-halves around. We just take it day by day with him and see how he progresses."
The 30-year-old is out of contract at the end of the forthcoming season and the new Premier League rule that clubs must name a 25-man squad for the season also complicates his situation.
Should Woodgate make a full recovery he is not guaranteed a starting spot with the likes of Michael Dawson, Ledley King, Sebastien Bassong and Younes Kaboul all battling for places.
Source: PA
Source: PA