Mr Morrison was responding to a speech by Labor senator Penny Wong who said straight politicians don't understand the level of abuse same-sex people cop.
Senator Wong, who is in a same-sex relationship and has a young family, declared she was not immune from the abuse thrown her way but was resilient enough to withstand it.
But many were not, and a national plebiscite on same-sex marriage could cause significant harm.
"I oppose a plebiscite because I don't want my relationship, my family to be the subject of inquiry, of censure, of condemnation, by others," she said in a speech at the Australian National University overnight.
"I don't want other relationships and other families, to be targeted either."
Mr Morrison said he respected Senator Wong's concerns.
But he pointed out that people with strong religious views who oppose same-sex marriage were also targets of dreadful hate speech and bigotry.
"I know it from personal experience having been exposed to that sort of hatred and bigotry for the views I've taken," he told ABC Radio on Wednesday.
Opposition Leader Bill Shorten attacked the way Mr Morrison injected himself into the debate.
"I think it is regrettable that Scott Morrison felt the need or the depravation to include himself in Penny Wong's remarkable speech," he told reporters in Sydney.
But Mr Shorten acknowledged that sometimes people of faith faced criticism for their views.
Prime Minister Malcolm Turnbull believes the plebiscite will be conducted in a respectful manner.
"The big difference, I think, between me and Mr Shorten on this is that I respect the common sense and the values and the decency of the Australian people," he told reporters in Cairns.
Mr Turnbull has come under attack from conservative Liberal Cory Bernardi, who has criticised the prime minister's response on the ABC's Q&A program when asked about homophobia within the coalition.
"By saying he'd had firm discussions with a number of colleagues, Turnbull gave implicit support to the claim that myself and other coalition MPs are homophobic," Senator Bernardi said.
"For the record I have never had such a conversation with any of my colleagues." Senator Bernardi said disagreeing with something doesn't constitute a "phobia".
