Blackwell said: "He has got a bad groin. I asked him to play and it did affect him first half.
"But he showed that team spirit and character to play. Depending on the severity, it could be four or five weeks."
The Blades sold central defender Matt Killgallon to Sunderland on Friday and 24 hours later saw Marcel Seip strain his hamstring in the warm-up prior to the FA Cup defeat at Bolton and Blackwell is keen to draft in cover.
He added: "(Jonathan) Fortune is out on his feet and I didn't expect that 'Killa' and Seip would both go on the same weekend," he said. "I have got to try and get another centre-half in and if I can I will. But it's proving difficult at the moment."