The 33-year-old, who was recently dropped from the England squad, signed for Delhi for a bid in the region of £880,000 in February.
Pietersen, who suffered the injury during pre-season with county side Surrey, replied to a Twitter user claiming that he will not undergo surgery and is closing in on a return.
The batsman tweeted: "I'll play this week hopefully! Pain is weakness leaving the body!"
Delhi's next fixture is against Chennai Super Kings at Zayed Cricket Stadium.