Williams tweeted this afternoon that he intends to clarify his position during the week.
The spokesperson was not aware of any similar objections being lodged by other players.
The NZR were unaware that SBW would put a plaster over the BNZ sign on his collar for his debut against the Highlanders in Dunedin on Saturday night, but there would be no misconduct charge, and the spokesman said it was "an issue for the Blues".
SBW has not declared why he covered up the logo but speculation is rife it relates to his Muslim faith, which is opposed to gathering interest on fees on loans.
Blues assistant coach Steve Jackson said he was surprised by the act and his team would be addressing it with Williams' management this week.
"The sponsors pay our wages and you look to do everything you can to make them happy, so I'm not really sure what occurred or what's really happened," Jackson told Newstalk ZB's Tony Veitch.
Williams converted to Islam in 2009, a religion which frowns upon borrowing money or paying interest to banks.
The rules surrounding money lending lie in the principles of Islam's shariah law.
As a matter of faith, a Muslim is not allowed to benefit from lending or receiving money, meaning earning interest is disallowed.
Boxer Anthony Mundine borrowed $500,000 from Williams before his fight against Danny Green in February, to deal with a family emergency, the Daily Telegraph reported.
The deal was sealed with little more than a handshake between two long-term friends.
Mundine gave the Blues player $750,000 in 2008 when he stormed out from the Canterbury Bulldogs to play French rugby union.
A BNZ spokeswoman said the bank had no issue with their logo being covered up.
"It's really between him and the Blues - we've got no issue with it," she said.
"He's entitled to have religious beliefs and customs around that and it's really between him and the Blues as to how that manifests itself. So we have no issue with it."
Williams is not the first sports star to have refused sponsorship on his uniform.
Pakistani-born Australian cricketer Fawad Ahmed has refused to wear the team's shirt which had a VB beer logo on it. Australian batsman Usman Khawaja followed suit and had his cricket gear modified to not show the VB or XXXX beer logos, according to The Courier Mail.
Prior to tonight's match Williams shared a photo of his jersey on social media. The personalised jersey is embroidered with the names of his wife Alana and two daughters Imaan and Aisha.