Walker played the whole Champions League match in Turin but could not help Pep Guardiola's team avoid a seventh defeat in 10 matches.
The England international posted a screenshot of a message he received on Instagram from an unnamed user to his social media accounts on Thursday that used obscene racist language.
"No one should ever be subjected to the sort of vile, racist and threatening abuse I have received online since last night's match," Walker wrote on his X and Instagram accounts.
"Instagram and the authorities need to stop this happening for the sake of all who are suffering this abuse. It is never acceptable.
"To our fans, we will continue to work as a team to do better, to improve and to turn the corner together."
City condemned the racist attack. A club statement read: "Manchester City strongly condemns the racist abuse that Kyle Walker was subject to online following last night's fixture.
"We refuse to tolerate discrimination of any kind, regardless of whether that be in stadiums or online."
A Premier League statement read: "The Premier League condemns all forms of discrimination. Racism has no place in our game or anywhere in society. We encourage anyone who hears or sees discriminatory abuse to report it so action can be taken.
"The Premier League will support Kyle Walker and the club to tackle online hate."
© 2024 AFP