Despite early fears that he could be out for a lengthy period of time, Parr believes that he could be back playing sooner rather than later.
"I am extremely happy that I am 100% well. It was a hard knock, but I am happy I have not suffered a serious injury," he told Sky Sports News.
"I hope to be back playing soon. I might not be able to play this Tuesday, but I am sure I will be ready next weekend."
Palace play Hull City on Tuesday and then face Arsenal on Saturday.