Pogba donned the band during the 4-1 triumph, and he said afterwards it was with the centre-back in mind. Koulibaly was the victim of racist abuse during the Partenopei's match against Inter Milan on Boxing Day, per Sky Sports.
"Well done guys, beautiful way to end the year and an honour handband for Kalidou Koulibaly. In 2019 say NO to racism," he said on Instagram.
The wristband was black and white, with "NO" written on it.
As Sky Sports relayed, Inter have been ordered to play their next two home matches behind closed doors following the incident. Koulibaly was subjected to monkey chants by some in the stadium.
Inter boss Luciano Spalletti condemned the abuse.
"Racist chanting should not be taking place," he said, per Dejan Kalinic of Goal. "If 65,000 people come and watch the match on Christmas, they want to see something else. This is the football that Italians and the people around the world want to enjoy."
Numerous figures in football have supported Koulibaly, including Napoli and Argentina legend Diego Maradona:
The Napoli players also warmed up for the game by wearing the 27-year-old's No. 26 jersey in another display of solidarity.
Pogba's gesture came in a 4-1 win for Manchester United, with the Red Devils coasting past Bournemouth. The Frenchman was the star man on the day, as he scored two goals and set up another. It was the second game in succession in which Pogba has netted a brace.
The former Juventus man has said in the past he was the victim of racist abuse in Serie A. In 2013, he accused Torino striker Riccardo Meggiorini of using a racially motivated insult, per Neil McLeman of the Daily Mirror.
In March this year, Pogba and his France team-mate Ousmane Dembele were also allegedly subjected to monkey chants when his side played against Russia in an international friendly, per Jamie Smith of Goal.