King is troubled by a persistent knee injury that restricts his ability to train but has put himself back into England contention with a string of superb performances in the Premier League run-in.
Redknapp is amazed how the centre-back, who is likely to be included in Fabio Capello's squad for South Africa, can churn out such displays in the circumstances.
"How a lad can not train but come out and play against top players as he has, I don't know," he said.
"It's defied all logic, it's amazing. If that's the way to do it, we're wasting our time coming into training every day - we might as well all just turn up on Saturday! He's a freak really, how he can do that."
King has played in Spurs' last three matches - including two in the past week - so Redknapp is likely to rest his captain for Sunday's match at Burnley.
Champions League football is now secure thanks to Wednesday's 1-0 win at Manchester City and Redknapp wants to make sure King does not sustain a fresh setback before Capello names his enlarged preliminary squad for the World Cup on Tuesday.
"I would not want to crock him," Redknapp said. "It is important that if he has got a chance of going to the World Cup, I don't finish him off."
Redknapp is already shaping his squad for next season's tilt at Champions League glory but he is delighted with what he has at his disposal, especially with loaned-out players such as Robbie Keane and Jamie O'Hara set to return in the summer.
"I would not lose any sleep if we don't do anything," said Redknapp, the Premier League's manager of the season.
"But if we can find a special player, I would say to the chairman or owner. It might only be one player.
"We are not going to sign Fernando Torres. But like Liverpool signed him, (we want) a player that could take you to another level. But where you find them, I don't know."
Source: PA
Source: PA