Knee sprains can take anywhere from 2 to 4 weeks and up to 4 and even 12 months to fully heal up.
Typically though if the sprained knee is not too severe then you should start to recover from the sprained knee in a month which is 4 weeks.
At least that was the case with me when I sprained my knee last year. It started to recover in 4 weeks but took around 2 months to fully recover have the sprained knee heal up.
It entirely depends on how bad you sprained your knee though to know how long it will take the sprained knee to heal up.