When I did my MCL (partial tear) I could barely walk for a few days. If you're getting around fine it's unlikely to be ligament damage. From the description of the injury it sounds like a partial meniscus tear. I did this recently myself trying not to land on someone after I threw them.
I found that as long as you have good form squating should be fine, just don't do any weights that could compromise technique. I found stationary bikes to be quite painful as you exert force through the ball of the foot when riding rather than the heel and this puts pressure on the meniscus.
If the tear is near the edge then healing shouldn't take too long (4 to 6 weeks) and you can return to BJJ training before the end of the period as long as you are really careful.
Hope this helps.