The Muslim All Blacks midfielder's trip south means he will miss the Auckland-based franchise's Super Rugby match against the Highlanders at Eden Park on Friday night.
Assistant coach Tom Coventry said the coaches thought it would be a good idea, even before Williams made the request.
"We were going to ask Sonny if he'd like to make the decision to go.
"We were all in agreeance, it was a pretty short conversation.
"We all knew how hard he took it, so it was a simple decision to make."
Williams posted to social media on Sunday night saying he would be in Christchurch "later in the week to show love and give donations to the Christchurch Masjids for the people effected in this tragedy".
Coventry said that desire to make the trip, with the match Williams is missing counting as one of two games he must stand down this season as an All Blacks player ahead of this year's World Cup, said a lot about his character.
"His faith is strong. He felt for the people of Christchurch and obviously, he [has] had a lot to do with the Crusaders over his long career - he spent a couple of years down there.
"We admire what he's standing for and the fact he would like to go down there and grieve and be part of the support for the region and the people of New Zealand.
"It's just a sign of Sonny having a really caring side.
"Rugby is important to everyone but at the end of the day it's just a game and [that] region and our country probably come first when it comes to dealing with these sorts of issues."
Coventry said he felt the Blues squad and how it operated was an example of how New Zealand should be.
"If you look at the Blues, we're made up of a host of different cultures and nationalities. We embrace that and it's where New Zealand is at the moment.
"To see how we got on within our team, we have strong relationships between the different cultures and faiths.
"We're a microcosm of society, I suppose, and sport to me has always been a way of getting our children, getting our people involved in our community and embracing our community differences."