Aloke Aich, 53, was hit in the right eye during the match between Kolkata Knight Riders and Kings XI Punjab at Eden Gardens on 9 May.
"The incident and its ramifications have been terrible." Miller said.
"I wish this was not true - I am sorry for Mr Aich's irreversible loss and wish him the best recovery possible."
Aich's son said that Kolkata Police were paying his father's medical expenses but also said that he feared the injury might force his father, the sole earning member in the family, to give up his job.
"I don't know what will happen. With his right eye gone, I don't think he would be able to sit behind the wheel again," he told the Indian Express newspaper.
"Will they keep him in the job or will he be asked to take voluntary retirement? How will we survive if he loses his job?
"We are a lower middle-class family, dependent solely on his income."
Miller scored 27 not out from 11 balls in the match in question, which Kolkata won by one run.
The 25-year-old first joined Kings XI Punjab in the IPL in 2011, and hit a 38-ball century against Royal Challengers Bangalore at Mohali in May 2013, the third fastest hundred in the history of the tournament.
The left-hander has appeared in 71 one-day internationals and 31 Twenty20 internationals for South Africa.
A policeman has been left blind in one eye after being hit by a six struck by South Africa batsman David Miller in an Indian Premier League match.