The 62-year-old has lost almost three stone in recent months and was urged to visit doctors by his wife Catherine and other family members.
He is now receiving treatment for what is most likely to be Type 1 diabetes and awaits further tests.
Sir Lindsay said the diagnoses “is still a shock” and his family are “very worried”, but said he is determined to continue his roles as an MP for the Lancashire seat of Chorley and as the new Speaker.
Speaking to ITV News, he said: "I have got diabetes. Yes I have to take insulin every day, I'm having to inject; very hard for me but I think that shows not only can I do this job but actually it's to try and help others."
Sir Lindsay cited former Prime Minister Theresa May, who also has Type 1 diabetes, as an inspiration and says family and Commons’ staff have been very supportive.
"She dealt with it very easily. The fact is, she was prime minister, she got on with the job, didn't affect her. In the same way I want to show people, yes I can do this job, yes I have a condition, but it's not going to stop me, it's not going to affect me."
He earlier said: “I’m on tablets, as well as having to inject insulin, but it doesn’t stop me carrying on and nothing is going to be a barrier to me.
“The fact is I feel really well. We know what it is – that’s the good news – and of course, I have got to get over it and get on with my job.
Sir Lindsay said he decided to go public about his health condition during an interview with Rob McLoughlin for the forthcoming series Mr Speaker.
Chris Askew, chief executive of Diabetes UK, said: “Living with Type 1 diabetes can be hard, but as Sir Lindsay’s experiences have shown, with the right support from your healthcare team – and careful management – people can live full and healthy lives following their diagnosis.
“It’s often thought that Type 1 diabetes only affects children but, while it’s less common to see someone of Sir Lindsay’s age diagnosed, it can affect a person at any time in their life.
“That’s why knowing the signs and symptoms of diabetes – the four Ts – can be a life-saver.
“So if you’re going to the toilet a lot, experiencing increased thirst, are more tired than usual, or losing weight without trying, you should speak to a healthcare professional.”