Jones-Drew has missed five consecutive practices, didn't travel to Tampa Bay last week and didn't dress for Thursday night's preseason finale against Atlanta.
He denied an Internet report he had arthroscopic knee surgery, but acknowledged that he has been "taking care of all the nicks and bruises."
"I wanted to be out there with my teammates, but we felt the best thing for me was rest and rehab and getting my body back right ..." Jones-Drew said. "I feel great. I can't wait to get out there and play Denver. They are the first hurdle in our road to success and I can't wait to get out there."
He called the false report "a big mess over nothing."
"There have been some false reports out there about what happened, which is fine," Jones-Drew said. "People are going to speculate, but that is not going to hurt anything that happens with this team. More than anything else guys understand. They want me back, I want to be back, and I will be back on Monday doing everything I need to do to get ready to beat Denver."
Jones-Drew started every game last season and finished with a career-high 1,391 yards and 15 touchdowns. He carried 312 times and ranked third in the NFL with 365 touches, trailing only Tennessee's Chris Johnson and St. Louis' Steven Jackson.
Coach Jack Del Rio wants to limit his touches this season, with backup Rashad Jennings sharing more of the workload.