How long could knee arthroscopy recovery take?

It Depends. On how active you are and how much was done during surgery. For a routine knee scope i typically allow my patients back to work in 3-4 days if they have a sedentary job. Otherwise, most people can start getting back to work at 2-3 weeks depending on their job. Strengthening of the quadriceps muscle is key as this shuts down with knee surgery of any kind. Most people are near full by 4 weeks.
Depends on Diagnosis. Arthroscopy is a method used to treat knee problems - a wide variety of procedures can be done 'through the scope' depending on what is seen - from simple 'clean out' of a meniscus tear to meniscus repair to cartilage healing procedures. The recovery can be from a week or so to many months. Ask your surgeon exactly what the plan is after surgery so you best understand what to expect.