Heath, 32, was injured in training just before United's Women's Super League clash against Chelsea on Jan. 17.
"Unfortunately it is a longer one," Casey told a news conference. "We are looking at 10 to 12 weeks from the injury.
"It is a part of the game. She was a big player for us so she is a big loss. But, as all injuries, I always say it is a window of opportunity for somebody else.
"Disappointing for her but she is still heavily influential in our environment and we will work hard to get her back as safe and as quick as possible."
The SheBelieves Cup runs from Feb. 18-24. Heath, alongside United teammate Christen Press, had previously opted not to travel back to the United States for Vlatko Andonovski's January camp.
Andonovski has to yet to announce his roster for the tournament where the USWNT will play Argentina, Brazil and Canada after Japan withdrew due to COVID-19 concerns.
"Sam's come back and I think it's kind of just working out with a scan which is kind of remnants of an old injury and which is kind of a new injury, because she's showing quite well to be honest," he told a news conference on Friday.
"She's looking good. She's come through a few checks. I think this weekend [against West Ham] will be too soon for her, but there's a real possibility that she could be back at the back end of next week and ready for the game after that."
Taylor said that it was important not to load players too much but also to listen to their instincts about injuries.
"We need to make sure that we're not pushing players too much too soon, but Sam's a very positive person," Taylor added. "Even when she was given the news about her injury, she felt that it was better than what that was showing. That just speaks volumes of the person [she is] really.
"She's a very positive person and she's working really hard to get herself back in."