The 29-year-old England right back also breached social distancing measures put in place by the government to control the spread of the Coronavirus pandemic, which has killed close to 5,000 people in the country.
Walker becomes the latest English footballer to fall foul of the rules after Aston Villa’s Jack Grealish similarly crossed the line last week.
City said in a statement: "Manchester City FC are aware of a story in a tabloid newspaper regarding the private life of Kyle Walker in relation to a breach of the UK lockdown and social distancing rules.
"Footballers are global role models, and our staff and players have been working to support the incredible efforts of the NHS and other key workers in fighting the effects of the COVID-19 coronavirus, in any way we can. Kyle's actions in this matter have directly contravened these efforts.
"We are disappointed to hear the allegations, note Kyle’s swift statement and apology, and will be conducting an internal disciplinary procedure in the coming days."
Walker, who joined the champions from Tottenham Hotspurs in 2017, has apologised for his actions.
"I want to take this opportunity to issue a public apology for the choices I made last week," Walker told The Sun.
"I understand that my position as a professional footballer brings the responsibility of being a role model.
"As such, I want to apologise to my family, friends, football club, supporters and the public for letting them down."
