Mr Dimbleby made his dramatic statement at the start of the show right after introducing the five panellists.
No Government Minister appeared to defend its record, with the Conservatives instead being represented by backbench MP and deputy party chairman James Cleverly.
Noting this Mr Dimbleby said: “It’s very nice to have James Cleverly here.
“But I do think it’s a bit odd in this particular week that not one member of the Government, not one Cabinet Minister, would come on Question Time and talk to an audience of voters.”
Mr Cleverly replied, to Mr Dimbleby’s amusement: “Well if they had I wouldn’t have been able to be here and I love being here with you.”
Last night’s Question Time was broadcast from Guilford in Surrey.
Also on the panel were Labour’s Shadow Brexit Secretary Keir Starmer, journalist Zanny Minton Beddoes, writer and former Thatcher advisor Lord Dobbs and comedian Nish Kumar.
During the show the state of the ongoing Brexit negotiations, the UK’s relationship with Saudi Arabia following the disappearance of Jamal Khashoggi, transgender rights and whether John Bercow should resign as House of Commons speaker were debated.
The lack of a Minister to explain the Government’s position was also criticised on social media.
David Williams, from Wiltshire, tweeted: “No Government Minister on BBC’s Question Time.
“They are in total meltdown. Simply failing at every level.”
Meanwhile, Dr Belinda Brooks-Gordon, a Birkbeck University academic, commented: “No Government Minister on BBC Question Time cowardice”.
During the show Mr Starmer claimed the Brexit negotiations “are a complete mess” and argued “we have to accept we are economically close to the EU and should be”.
Mr Cleverly argued for a clean Brexit stating: “It was a binary choice and there’s no half leaving or half remaining.”
The Brexit talks are currently stalled over how to avoid a hard-border between Northern Ireland and Ireland or any checks between Northern Ireland and the rest of the UK.
EU leaders have decided not to call a special Brexit summit in November as they claim the UK has made “insufficient progress”.
Mrs May suggested yesterday that the Brexit transition period could be extended “for a few months” to allow the Irish border question to be dissolved.