Benn, 26, had a career-high 89 points on 41 goals and 48 assists last season. He also had five goals and 10 assists in 13 playoff games.
"Jamie has evolved into one of the most complete players in the NHL, and his ability to lead our team is second to none," Nill said in a statement. "He impacts the game in so many ways, and this signing was extremely important for the direction of the franchise. ... He's our leader and does things the right way, every day."
Nill said the full recovery time for the abdominal injury is six weeks. It wasn't clear when or how Benn got injured.
That timeframe puts Benn on schedule to be ready for the NHL season, but creates uncertainty about his availability to participate for Canada in the World Cup of Hockey that begins in mid-September.
Benn has 192 goals and 256 assists in 508 career games.