O'Mara, who represents Sheffield Hallam, said he would be missing important debates at Westminster this week, including votes on Brexit.
"Following a deterioration in my health and wellbeing over the past few days, and following a consultation with my GP, I have been advised to curtail my parliamentary duties in Westminster for the time being," he said in a statement.
"I recognise that these are important times for our country in relation to Brexit negotiations. I therefore contacted the Speaker's Office to ask if they were able to make a reasonable adjustment to allow me to vote in the debates taking place in Parliament this week but, unfortunately, this has not proved possible. I am very disappointed that I have been excluded from being allowed to represent my constituents in Sheffield Hallam in such a way. I will continue to pursue this matter and am working hard to get myself back to full health."
A spokeswoman for the Speaker’s Office said: “The Speaker has no power to allow absent Members to vote by proxy.”
O'Mara was suspended from Labour in October, following the discovery of misogynistic, homophobic and racist online comments he posted in his twenties, as well as the allegation he called a woman an ‘ugly bitch’. Two weeks ago he was reinstated by Labour and told to attend mandatory training, but last Thursday he resigned from the party, saying he felt as if he was 'treated like a criminal' during his suspension and claiming he had 'not been listened to'.
“I am of the opinion the Labour Party no longer shares my commitment to the true definition of equality and compassion,” he said in a letter to constituents. He pledged to remain as an independent MP.
News of O’Mara’s resignation emerged 48 hours after he gave an interview to ITV, in which he revealed he had tried to take his own life three times during his suspension, that he struggled with autism and admitted once being an internet ‘troll’. The MP, 36, became tearful on camera as he said he had become closer to his mother, stating: “I love my mum.”
In his letter, he added: “I believe I am the first autistic MP in our history, and this sadly got lost in the narrative of my interview with ITV. I ask for everybody to go on the internet and read about autism, and about my other disabilities; clinical depression, cerebral palsy and anxiety."