The media personality, who has been accused of making several offensive remarks in the past, said it was "ridiculous" to live in a country "where we can put dogs to sleep but not people".
In an interview with Michael Buerk in the Radio Times magazine, Hopkins said: "We just have far too many old people."
She added: "It's ridiculous to be living in a country where we can put dogs to sleep but not people."
Asked for her solution, she said: "Easy. Euthanasia vans - just like ice-cream vans - that would come to your home."
The former Celebrity Big Brother contestant added: "It would all be perfectly charming. They might even have a nice little tune they'd play. I mean this genuinely. I'm super-keen on euthanasia vans.
"We need to accept that just because medical advances mean we can live longer, it's not necessarily the right thing to do."
Louise Morse from the Christian charity Pilgrims' Friend Society said the comments were "wicked and evil".
On Premier's News Hour she said: "My first reaction was who is Katie Hopkins?
"There's nothing in her background to show that she has any experience of older people or any understanding of them at all.
"In fact she seems to gain exposure by making wild claims.
"In a nutshell I think this is just another shout by Katie Hopkins to get noticed because there's nothing about her that would get her noticed any other way."
She added that it was a "dreadful" thing to say and that the media personality "doesn't think before she opens her mouth".
"Older people are hugely affected by the negative things that are said and that they read about them.
"We're all affected by feedback of this sort, whatever your age.
"So for older people you'll get two reactions, one will be very cynical and say 'oh what do they know they're at it again'.
"The others will take it on board and think less of themselves and I think that's an extremely wicked and evil thing to do."
Louise Morse speaking to Antony Bushfield on Premier's News Hour: