The 31-year-old 800m and 1500m athlete from Cornwall competed in the 2014 Commonwealth Games and 2008 Olympics.
"I won't be able to run until at least April and then it's qualifying. It's a big ask," she told BBC Radio Cornwall.
"This was going to be my last push to make a real go at the Olympics - there was a real opportunity to go to Rio."
Simpson, who considered retiring in 2014, snapped her posterior tibial tendon - which supports the arch of the foot - in training.
She has been operated on by specialist foot surgeon James Calder, who has previously treated the likes of footballer Jack Wilshere.
"I'm not confident (of selection for the Olympics). It would be a miracle to do that now because I have to run the qualifying time and be ready for the trials, which is in seven months, and I've got three months off," added Simpson.
"I didn't feel any pain necessarily, but I heard something and my foot went limp - then I knew I'd done something quite major.
"It's hard to take the decision in your mind to stop, without having a reason to stop. It's hard to explain but when you have something like this, it takes the decision out of your hands."
Great Britain middle distance runner Jemma Simpson says she will need a "miracle" to make the Rio Olympic Games after rupturing a tendon in her foot.