One person replied: "You're disgusting too then, because you're are also white."
Others branded her a 'hypocrite' and a 'racist', with another commenting: "You shouldn't stereotype.. ppl are different regardless of colour !!!!"
Muslims on Twitter said she was misinterpreting the religion and one used the hashtag #notintheirname.
O'Connor announced she had converted to Islam late last month, posting images of herself wearing a hijab and a video of her reciting the call to prayer.
Today her tweet read: "I'm terribly sorry. What I'm about to say is something so racist I never thought my soul could ever feel it.
"But truly I never wanna spend time with white people again (if that's what non-muslims are called). Not for one moment, for any reason. They are disgusting."
Responding to the comment, one Muslim Twitter user posted: "Islam doesn't hate or dislike people on basis of their colour.
"You must change this thinking Shuhada. Allah is merciful and Prophet Muhammad (saaw) taught us kindness for all."
Another wrote: "So you convert to Islam and now you don't want to spend time with white people?"
"If you really think that you're an embarrassment to Islam, and I for one would not want you tarnishing my religion with this hate speech #notintheirname"
One person commented: "Islam does not allow u to be a racist. And logically It also does not allow u to generalise.
"U can't judge millions because of a few, whatever colour they may be."
Referring to the negative comments, O'Connor posted again: 'Forgive me. Sometimes the Lord needs dirty workers ; )'
In late October, the mother-of-four who was ordained as a Catholic priest in the 1990s, wrote: 'This is to announce that I am proud to have become a Muslim.'
She added: "This is the natural conclusion of any intelligent theologian's journey. All scripture study leads to Islam. Which makes all other scriptures redundant. I will be given (another) new name. It will be Shuhada."
O'Connor also changed her twitter profile image to a Nike tick with the caption "wear a hijab. Just do it."
The singer said she was given her first hijab by her friend Elaine and 'got chills all over' her body when she put it on.
O'Connor has had a well-documented battle with mental health problems, which have been fuelled by a number of marriage break-ups and legal issues.
The mother-of-four revealed she attempted suicide in December 1999 on her 33rd birthday.
In October 2007 she revealed she had been diagnosed with bipolar disorder four years earlier and has had a number of stints in rehab facilities across the USA.
In August 2016 she posted a distressing 12-minute video online saying she felt alone after losing custody of her 13-year-old son and threatened to kill herself in a New Jersey hotel room.
Police were scrambled to the Travelodge, but her management later assured fans, including musician Annie Lennox, she was not suicidal and received medical treatment after filming the clip.
She has been married four times and had children with four different men.
The former rock star last year claimed her late mother was 'possessed' and repeatedly sexually abused her as a child.
A member of her family also reported her missing in 2016 over fears she was suicidal. She was found in a Chicago hotel room.
In recent years she has largely stayed away from her native Ireland where her four children Roison, Sahne and Yeshua live, in favour of the US.
Her former lover and manager Fachtna O'Ceallaigh, 70, is currently suing her for defamation and breach of contract after she published a damning open letter to him online.
He claims O'Connor terminated their business relationship without warning and defamed him with the letter, for which he is seeking damages of around £452,000.
It was recently reported the singer will represent herself after sacking her lawyer.
