Cudd suffered the problem in the pre-season defeat to Scottish Guinness PRO14 rivals Glasgow at Ebbw Vale’s Eugene Cross Park home.
The 28-year-old needs an operation to fix damaged knee ligaments and is set to miss most of the campaign ahead.
Dragons head coach Jackman said: “Nic is out for pretty much the whole season and needs an operation.
“We will miss him a lot because he is a quiet leader and defensively he is outstanding, but it’s an opportunity for someone else.”
Dragons were beaten by Leinster on the opening week of the PRO14 and travel to Edinburgh on Friday night.
Wales flanker Ollie Griffiths is set to return for the game in the Scottish capital following a slight hip knock.
Griffiths and James Benjamin are now the senior men available to Jackman competing for the Dragons No 7 jersey.
“I thought James had a big game against Leinster and his tackle stats and breakdown work were outstanding,” said Jackman. “We like him a lot and he is a different type of player to Cuddy.
“And it’s an opportunity for Lennon Greggains at 18 to potentially play for his region and we’ve got to fast track him as coaches.
“It’s a big ask, but it’s exciting to see these rough diamonds and try and polish them quickly.”
