Chubb was placed on injured reserve, but Stefanski said that he expects him to return at some point this season.
A source told ESPN's Adam Schefter that doctors believe Chubb will miss about six weeks.
"What that ends up being, I don't know," Stefanski said when asked if the six-week timetable was accurate. "I know Nick Chubb, and I wouldn't put a time frame on it yet.
"Knowing Nick, he's gonna work very hard in rehab. I know that's hard to see your teammate go down like that; but knowing Nick, he will work his butt off to get back."
Chubb was injured in the first quarter of Sunday's 49-38 win over the Dallas Cowboys. He was pass-protecting when defensive lineman Trysten Hill rolled over his knee from behind. Chubb, who entered the weekend fourth in the NFL in rushing, had already run for 43 yards on six carries against Dallas.
The offense didn't miss a beat without him: Cleveland finished with 307 rushing yards, its highest game total in 11 years. D'Ernest Johnson led the Browns with 95 rushing yards, and Kareem Hunt ran for 71 yards and scored two touchdowns. Wideout Odell Beckham Jr. scored a 50-yard touchdown on a reverse to put the game away late in the fourth quarter.
Hunt is expected to take over as Cleveland's primary back with Chubb out. Hunt won the NFL rushing title in 2017 with 1,327 yards for the Kansas City Chiefs.
The Browns now lead the NFL with 818 rushing yards. According to ESPN Stats & Information, that is the fourth-highest total through the first four games of a season over the past 30 years. Only the 2005 and 2006 Atlanta Falcons and last year's Baltimore Ravens rushed for more yards over the first four games.