When asked what improvements he would make to the monarchy, the Labour leader cited "the size of the family and all that they do".
Asked if he thought it was too big, Mr Corbyn told Sky's Sophy Ride on Sunday programme: "Well I think there's a lot of people attached to the Royal Family."
Foreign Secretary Dominic Raab told the same programme he thought the suggestion was "crazy".
"We need to be respecting the institution of the monarchy and if Jeremy Corbyn is saying he wants to cut the number of the Royal Family he should come out and say who he wants to cut," he said.
Prime Minister Boris Johnson said earlier in the general election campaign that the Royal Family was "beyond reproach", before later clarifying that he was referring specifically to the Queen.
Last month, Prince Andrew stepped back from public duties for the "foreseeable future" over his links to billionaire sex offender Jeffrey Epstein.
The announcement came days after the prince's widely-criticised TV interview which saw Andrew accused of "utterly lacking in compassion" for the victims of Epstein, who killed himself earlier this year.
Away from the Royal Family, the Labour leader was pressed on a number of other subjects during a wide-ranging interview with Sky News.
In the wake of Friday's London Bridge terror attack, Mr Corbyn said convicted terrorists should "not necessarily" automatically serve their full prison sentences.
On Brexit, he confirmed he would vote in his proposed second referendum.
Mr Corbyn has pledged to stay neutral during the campaign itself.
Asked if he would reveal to the public how he would vote, he replied: "You'll have to wait and see."
Labour's antisemitism row returned to the headlines earlier this week, when chief rabbi Ephraim Mirvis said Mr Corbyn's claims to be tackling the presence of it within the party were a "mendacious fiction".
Mr Corbyn said he "wished our party had acted on it more rapidly at the very beginning and dealt with it at that point".
Polling by the Campaign Against Antisemitism, published in the Sunday Telegraph, found 84% of respondents regarded the Labour leader as a threat to British Jews.
Asked for his response to the poll, Mr Corbyn said: "I pose no threat to any community whatsoever in this country. I've spent my life fighting racism, fighting against racist attacks...
"I simply say this: there is no place anyway for antisemitism in our society ever."
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