The versatile Northern Ireland international had surgery in London and Leeds have said the 31-year-old will now undergo further tests.
Posting a picture on Twitter from his hospital bed, Dallas said: “Huge thank you for all of the messages I've received in the past few days.
“I've had amazing support from across the world of football – but particularly from Leeds and Northern Ireland. I'd also like to thank Dr Williams, Dr Sarraf and the medical team at @LUFC.
“The support I've received has meant the world to me and my family.
“Now it's time to focus on my rehab, I will be back from this stronger than ever.
“In the meantime I'll be supporting my teams every step of the way."