Wheeler's comments lead to an avalanche of condemnation from Sky Sport viewers.
Race Relations Commissioner Meng Foon also came out against them on Saturday, saying they were hurtful and had no place in society.
As the Super Rugby Aotearoa prepares for this weekend's clashes – with the Highlanders playing the Chiefs on Saturday, and the Hurricanes facing the Crusaders on Sunday – a spokesperson for Sky said Wheeler would not be behind a microphone.
"Joe Wheeler has apologised for his comments and Sky has made it clear where we stand," the spokesperson said.
"Joe has acknowledged that he has some work to do and we're supporting him through this. Joe is off air at this time."
About an hour after making his controversial comments, Wheeler took to social media to apologise.
"Tonight I stuffed up! I've spoken with @teikyo_8 (Kazuki Himeno) and apologised to him and the @Highlanders and our Sky crew. I absolutely accept this is not the standard expected of the sideline team. I've got some work to do obviously, but I'm absolutely committed to doing better," he wrote on Twitter.
That tweet was followed by a statement from Sky to the media.
In it, the broadcaster wrote: "Joe Wheeler has spoken with Kazuki and apologised to him and to team management.
"He absolutely accepts this is not the standard expected of the broadcast team.
"Sky is committed to being culturally respectful and we expect all crew to do the right thing."
As well as being slammed by many Sky Sport viewers, international media picked up on Wheeler's comments; including several leading Asian websites.