But Woodward has left the door open, stating the England captain could still travel if he regains full fitness, which also applies to centre Mike Tindall (foot) and prop Phil Vickery (broken arm).
"If they confirm genuine form and fitness in the coming weeks, they could still go," said Woodward.
"My thinking is it is better they try to do so with their clubs before becoming part of the Lions squad.
"At their very best and fully fit, all three would have made the squad and their absence from the list does not necessarily rule them out from the tour.
"I have spoken to the players and they agree with this approach.
"I clearly know how much Jonny wants to play and I think this is the best way of keeping that prospect alive.
"If he makes it, all well and good but his appearance in the Test team is not guaranteed.
"He could have played last week but decided to delay it. He is one of the most mentally tough people I've come across and no doubt he'll get back to his best, it's just the timing of it.
"He's an exceptional player. If he comes through the next six games with his club, then he will be included in the squad.
"I had a chat with the other three fly-halves (Stephen Jones, Charlie Hodgson and Ronan O'Gara) and they fully support my decision. If he does make it, he is in for a hell of a fight to displace the other three players."
As expected, Ireland's Brian O'Driscoll has been appointed captain, and there are places for England World Cup stalwarts Neil Back, Lawrence Dallaglio and Richard Hill.
Leicester flanker Back, 36, becomes the oldest player in Lions history selected for an original tour squad.
Several young England prospects have also received the nod, including Leicester centre Ollie Smith, Sale front-row forwards Andy Titterrell and Andrew Sheridan and Bath prop Matt Stevens.
O'Driscoll heads a strong Irish contingent, while Six Nations champions Wales have 10 Lions but Scotland are confined to scrum-half Chris Cusiter, hooker Gordon Bulloch and back-row forward Simon Taylor.
Woodward has chosen 14 of his victorious 2003 England World Cup squad, and nine of the World Cup final starting XV, but he was at pains to point out the Welsh and Irish strengths.
"If we were playing this weekend, the majority of the starting XV would come from Wales and Ireland, with two players from England and one from Scotland," he added.
"So people should not read too much into the national make-up of the squad, which incidentally, is very similar to that of the last two Lions tours.
"Being picked for the Lions is the ultimate honour, and a New Zealand tour is the ultimate challenge.
"The players we have announced are world-class, and the best in the British Isles and the right squad to take.
"We believe we can win. If we win the Test series it will be an achievement to match anything else we have done during our careers."
The England contingent includes centre Will Greenwood, who makes his third successive Lions trip after recovering from shoulder surgery, and full-back Iain Balshaw also makes it, despite an injury-plagued last 12 months.
The Irish representatives are predictable and Wales' Grand Slam stars are out in force - Jones, Gareth Thomas, Gareth Cooper, Dwayne Peel, Gavin Henson, Tom Shanklin, Shane Williams, Gethin Jenkins, Martyn Williams and Michael Owen all make the trip - but there is no place for Colin Charvis.