New Zealand captain Williamson out of 2nd Test against England
However, the Blackcaps are confident he will be fit to lead the team in the inaugural World Test Championship final against India starting on June 18.
"He's had an injection in his elbow to relieve the irritation he's been experiencing when he bats and a period of rest and rehabilitation will help maximise his recovery."
Stead added: "The decision has been made very much with the ICC World Test Championship final at Southampton in mind and we are confident he will be ready for that match starting on June 18."
"Someone of his (Williamson's) leadership, his calibre as a player, it's obviously disappointing that he's been ruled out to nurse his elbow injury," Latham told reporters.
"He doesn't get too high, and doesn't get too low, which has been great for this side over recent years... He'll certainly be missed," added Latham, looking to lead New Zealand to their first series win in England since 1999.
"He's a big gun, number one in the world," said Root. "He's one of those players you spend a lot of time thinking about how you're going to keep him quiet and get rid of him early.
"We saw last week a debutant (Devon Conway) coming in and getting a double hundred."
But experienced left-arm quick Trent Boult is set to come back into the XI after missing the Lord's match, having opted to spend time with his family following the suspension of the Indian Premier League.
"It's great to have someone of his calibre come back in," said Latham of Boult.
"The way he can swing the ball, his leadership as well. He's been to this part of the world before and he knows how to perform (in England)."