Webb, 27, has not played since injuring a foot during a World Cup warm-up match against Italy in September.
Wales begin their Six Nations campaign with an away match against Ireland in Dublin on Sunday, 7 February.
Ospreys will also be without back row Tyler Ardron for eight weeks because of a knee injury.
The 24-year-old, who was injured while playing for Canada at the World Cup, had surgery in October.
Ospreys had hoped Webb would make an early return from injury and be available this month.
But, though he has returned to training, he is still short of match fitness.
"His recovery is going well and we're now concentrating on getting him to the physical level he needs to be in order to perform as we want," said Chris Towers, Ospreys' medical performance manager.
"He has begun running again, starting doing some skills work, and the focus is on getting him available for selection at the end of February, which would be five months post-op."
Webb, capped 16 times by Wales, has renewed his national dual contract with Ospreys and the Welsh Rugby Union.
He turned down offers from elsewhere to stay at the region for whom he made his debut in 2007.
Ospreys and Wales scrum-half Rhys Webb will miss the start of the Six Nations as his region say he will not return from injury until the end of February.