The left-hander will be shut down for at least the next three to five days for the treatment and is likely done for the season.
Britton has been pitching with the strain in his knee, but said a recent MRI showed that the injury had worsened over the past month.
He said the goal is to have the PRP treatment and avoid offseason knee surgery.
Britton, 29, recorded 15 saves in a season that was interrupted by a forearm strain. He also saw his AL-record streak of 60 consecutive saves converted come to an end in August.