Harris injured his right knee on the second play of Friday's preseason opener against the Jacksonville Jaguars. He had to be carted off the field.
"Nick is certainly a guy who has worked so hard this offseason, so we're really hoping that it's not a season-long thing because the kid has worked so hard," Stefanski said Saturday.
"Ethan went in there and did a really nice job," Stefanski said. "He's been with us since April. We went out and got him for a reason and we're excited about what he did last night."
Harris was slated to be the lone new starter on the Browns' offensive line, replacing veteran JC Tretter, whom the team released in March.
The Browns drafted Harris in 2020 in the fifth round out of Washington. He made one start for Cleveland in each of the past two seasons at guard.
Tretter, president of the NFL Players Association, remains unsigned. The 31-year-old started all but one game, because of COVID-19, for the Browns the previous five seasons. Cleveland cleared $8.25 million against the salary cap by releasing him. Stefanski did not comment on the possibility of re-signing Tretter.