The clip, produced ahead of New Zealand's clash with France on Saturday, features Savea staring down the barrel of a camera saying "on November 26, I will take on Paris".
But the match footage that flashes up during the video shows Fekitoa in action for the world champions, not Savea.
Adidas, which has sponsored the All Blacks since 1999, said it regretted the error.
"We sincerely apologise to all fans for any offence our promotional video may have caused," Adidas New Zealand country manager Quentin Bleakley said.
"We will be rectifying our video as soon as possible."
Both players share Polynesian heritage -- Fekitoa was born in Tonga, while Savea is a Wellingtonian with a Samoan background.
Further compounding the gaffe, Fekitoa is ineligible to play in Paris after receiving a one-match ban for a high tackle on Ireland's Simon Zebo last weekend.
It is not the first time an All Blacks sponsor has found itself in hot water.
When New Zealand were hosting the World Cup in 2011, Telecom NZ came up with a marketing plan urging fans to give up sex as a way of supporting the national team.
The "Abstain for the All Blacks" campaign was swiftly kicked into touch when the public labelled it crass and pointless.
With a winning percentage of around 80 percent -- the equal of any team in world sport -- the All Blacks are arguably New Zealand's strongest global brand, recognised even where rugby is not commonly played.
They have attracted global sponsors such as Adidas and US insurance AIG, which has had its name emblazoned on the All Black jersey since 2012.