The One Direction star appeared uncomfortable during his appearance on the show.
He accused the presenters of "proper going in" on him, as he was questioned about his time in the boy band, writing his debut album Walls, and music about his loss, and his reported feud with former member Zayn Malik.
Tomlinson lost his mother in 2016 shortly after the band went on hiatus, and last year his sister Felicite died of an accidental drug overdose.
When the interview was over, Tomlinson wrote on Twitter: "Defo wont be going on there again Haha! Love to all my fans for always having my back."
Walker replied: "Sorry you feel like that. It was nice to speak to you on #BBCBreakfast this morning. Can I ask what you are upset about?"
In response, Tomlinson said: "I was upset that you continued to ask me about my grief.
"It goes without saying how hard it is to lose both people so close to me. The least I ask is that you respect my decision of not wanting to be asked in interviews about something so painfull.
"I'm lucky enough to have a creative outlet for me to talk about grief this doesn't however give you the right to talk about it for gossip purposes."
Walker replied: "Hi Louis. We were asking you about the song on your new album about your mum.
"We know it's painful which is why we didn't dwell on it. No intention to upset you or be 'gossipy' about it at all. That's not our style on #BBCBreakfast."
During the interview he was asked about the personal nature of his album and he said: "It's the only way I really know, it's what I did in One Direction and what I've done on my own, I only really know to write honestly and from the heart.
"I don't really do, well, writing fiction, so I've just written about different stages of my life and tried to make it as relatable as possible."
He added: "I think because of where I started my career, on The X Factor, there has always been a camera on me, and I've always given a lot of myself, so it's kind of all I've known in my career really, so I almost use that to my advantage.
"I'm brave enough to talk about these things and it's worked out."
Minchin later asked him about his "spat" with Malik, prompting Tomlinson to say: "God, you're proper going in here today aren't you?"
When Walker replied: "You know people will be interested," he said: "Yeah they will, but people pick up on every little thing I say.
"I'm just not ready to have that conversation yet, and I think that is fair enough."
He was also asked about the possibility of the group getting back together, and Tomlinson answered: "You've ticked them all off now. You've gone trauma, Zayn, and now we are finally on this one, I like it.
"I will give you the answer I give everyone else, it's inevitable.
"I don't know when, we don't know when. I think we would be stupid not to get back together, but we don't know when. I've only just released my first album and that's what I'm here for."