The former England international required hospital treatment but has since been released and is recovering, Rangers added.
"I've suffered a significant bleed to my leg that needed hospital attention, thankfully that's now under control and will lead to a full recovery hopefully sooner rather than later," Butland posted on his Instagram story on Wednesday.
"Needless to say it's come at an awful time and I was fully focussed on helping us as a club. The most important thing now is supporting the lads and focusing on getting fit again as soon as possible."