Yes, but it depends.
I hate websites that make you dig for the answer to the question in the title.
You can play with torn meniscus, but it really depends on the grade of tear. In most cases, a slight tear will cause some discomfort, but you can continue to play sports.
Chipper Jones decided to play through the pain:
I woke up this morning feeling better than I have in a month. So strap it up and find out
What is the meniscus? It is a pad of cartilage in your knee. See the red arrows below.
What does the meniscus do? The meniscus acts as a shock absorber for your legs. It sits between your thigh and lower leg bones (femur and tibia). It distributes the upper body weight across the lower leg bones.
How many do you have? You have two meniscuses or is it menisci? Hey, it’s menisci and you had a medial and lateral (inside and outside). A little side note, take care of these little fellas. Later in life, if you suffer from osteoarthritis you are screwed.
How do you injure your meniscus? Most commonly, the injury is a tear and you can do this a number of ways. The most popular way is twisting your knee while trying to push off. What do you know? Chipper Jones does this all the time with his hitting.
How do you treat a torn meniscus? Rest, ice, physical therapy and more rest for slight tears. For major tears you’re looking at surgery.
You can definitely play, just have to be careful not to injure it further! It is recommended to allow the tear to fully heal before participating in sports activities.