The Sun reported that Walker had breached government guidelines aimed at curbing the spread of the coronavirus by visiting his sister and parents before going cycling with a friend.
Last month, the England international apologised and faced disciplinary action from his club after the same newspaper claimed he and a friend paid for two sex workers to visit his Cheshire home hours after he issued a plea on social media to follow government advice and "keep following the protocols."
After the publication of the latest story, Walker released a statement and said his mental health has not been taken into consideration.
"I have recently gone through one of the toughest periods of my life, which I take full responsibility for. However, I now feel as though I am being harassed," he said on Twitter.
"This is no longer solely affecting me, but affecting the health of my family and my young children too.
"In relation to the events on Wednesday, I travelled to Sheffield to give my sister a birthday card and present, but also to speak to one of the few people I believe I can trust in my life.
"She hugged me to remind me how much she cares and that I am loved. What am I meant to do -- push her away?
"I then travelled to my parents' house to pick up some home-cooked meals. Again, it's been an extremely tough couple of months for them: everything I've gone through in my life they have gone through with me.
"What have my parents and sister done to deserve their privacy being invaded by photographers following me to their homes? I constantly feel as though I am being followed. I don't even feel safe in the confines of my own home - why should they have to feel like that too? Who deserves that?
"I am in a privileged position as a role model and a professional athlete, and can assure you from my upbringing that I do not take it for granted. But at what stage do my feelings get taken into consideration?
"My family has been torn apart, this has been dragged through the press, and I ask: when is enough enough?
"At a time when the focus is understandably on Covid-19, at what point does mental health get taken into consideration, an illness which affects every sufferer differently? I am a human being, with feelings of pain and upset just like everybody else."
Walker is the second City player to speak out against the national press after teammate Raheem Sterling accused sections of the media of fuelling racism with negative portrayals of young black players in December 2018.