Coach Romeo Crennel said the surgery was a success and hopes Peek will be back for the regular-season opener Sept. 7 against Dallas.
An MRI revealed loose cartilage in the right knee.
Peek tore cartilage in the same knee in the opener last season, but played 14 games before undergoing offseason surgery. He missed two games with an ankle injury.
Peek, in his sixth NFL season and second with the Browns, started four games last year, making 24 tackles, and was expected to provide a pass-rushing threat from the left side. He had four sacks last year and has 14 for his career.
"You never know whether it will become chronic or not," Crennel said of the knee problems. "He'll do everything he can to play on Sunday. I'm looking forward to him rehabbing and being back for that Dallas game."
They were counting on a healthy, bounce-back year from Peek to take some pressure off Kamerion Wimbley on the other side. While Peek rehabs, free-agent acquisition Shantee Orr, David McMillan (one tackle in a three-year career) and seventh-round pick Alex Hall will get time at left outside linebacker.
"Orr shows up every day in practice making a play, doing something," Crennel said. "He's shown up rushing the passer some as an inside linebacker, as an outside linebacker. He does have some versatility, which is good."
Willie McGinest, 36, is entering his 15th season and is the starter at left outside linebacker. He has seven sacks in two years with the Browns and usually gave way to Peek in passing situations.
"Willie can still rush," Crennel said. "He'll surprise a lot of people."
McGinest has 101 career sacks, including 16 in the postseason.