Tottenham defender King suffered his latest injury in Sunday's 2-2 draw against Newcastle and had to be replaced by Sebastien Bassong after just half an hour at St James' Park.
Redknapp stated after the game that the influential defender was likely to be out of action for "a while", but King has now undergone a scan and the damage is not as bad as first feared.
It remains to be seen when King might be available to return, but Redknapp is relieved it will not be a lengthy absence as he faces up to a defensive crisis.
"Ledley has had a scan. He has a slight tear in his abductor. It's not too bad," Redknapp said.
"It's only a grade one tear, which is not so bad, so it shouldn't be too long."
Bassong and Younes Kaboul are Spurs' only two fit centre-halves ahead of Thursday's Europa League clash at home to Rubin Kazan, with King joining Michael Dawson, William Gallas and Vedran Corluka on the club's injury list.
"Central defence is a big problem for us," Redknapp said.
"We are really down to two central defenders.
"The problem is that we have no one who will be back fit at the weekend so if one of them gets a knock on Thursday, we will be bang in trouble for Sunday's game against Blackburn."