The incident on Wednesday was caught on video, which shows the woman falling backward. Stafford reacted with astonishment before turning around to walk the other way.
His wife, Kelly, could be seen looking concerned as she walked up to check on the photographer, Kelly Smiley. Many took to social media after the video circulated to criticize Stafford for not doing more to help her.
Smiley has since posted an update to Twitter, saying she fractured her spine when she fell.
A GoFundMe account has been set up to help pay for Smiley's medical expenses and camera equipment that was damaged.
The Rams and Stafford released a joint statement on Thursday:
"We have been in communication with Kelly Smiley since yesterday's incident and we are sorry for what happened. As we told Kelly, we will be covering all her hospital bills and replacing her cameras. We wish her a speedy recovery."