Henderson, who has been a shining light in what is turning into another season of under-achievement for the Wearsiders, sustained the injury shortly after setting up Kenwyne Jones for Sunderland's equaliser in the 1-1 draw on February 6.
Medical tests had to be delayed for swelling around the joint to subside with Black Cats boss Steve Bruce confirming the length of the lay-off today.
Bruce said: "Obviously we're glad there's no serious damage, but to be without a player like Jordan for six weeks is a blow.
"We can now get on with the rehabilitation process. Jordan is keeping his spirits up and he is prepared to work hard while he's out."
Capped at youth level by England, 19-year-old Henderson has clocked up 28 appearances this season, scoring twice.
His absence leaves Bruce with a midfield headache ahead of this Saturday's testing trip to Arsenal.
Lee Cattermole and David Meyler are suspended following their red cards against Portsmouth, Steed Malbranque is doubtful with a chest injury while Andy Reid is battling a hamstring problem.
However, both Kieran Richardson and Fraizer Campbell are expected to be available for the trip to the Emirates Stadium.
** READ MORE SUNDERLAND NEWS IN TOMORROW'S NORTHERN ECHO **