Stats NZ mailed out access codes so all New Zealanders would have the opportunity to fill the census out online.
They said the Blind Foundation was offering assistance to its' members, but they now realise not every blind person received support.
Census General Manager Denise McGregor said Stats NZ had learned a lesson about how to reach the blind community.
"We have not been able to reach everyone through the Blind Foundation, and we are sorry about that," she said.
"We are doing our best to make sure everyone in New Zealand has the chance to be counted."
Blind Foundation spokesperson Neil Jarvis said while they had more than 12,000 members, there were around 170,000 people who struggled with sight in New Zealand.
He said Stats NZ needs to be more prepared for the 2023 Census.
"They needed to talk to the disability community much earlier in the planning of the next census," he said.
"That way, there won't be a need for a work around solution which is basically what happened this time."
Blind man Jonathan Mosen, who started the petition, said Stats NZ should be able to email or text out access codes.
"I had to wait until someone from Statistics New Zealand came to my house to read the code to me," he said.
"It's a shameful waste of government resources."
Anyone can sign Mosen's petition which will be open until early April.