Coronavirus: PM's father Stanley Johnson criticised for lockdown trip to Greece
Stanley Johnson shared a number of pictures on his Instagram account on Wednesday, showing him arriving in Athens and at an airport in a mask.
He told the Daily Mail he was in the country "on essential business" to ensure a property he rents out was "Covid-proof" before holidays restart.
But the former Tory MEP has come under fire for breaking lockdown rules.
Liberal Democrat MP Jamie Stone said the incident "stinks of one rule for them and another rule for the rest of us".
The prime minster's official spokesman declined to comment.
The Johnson family dynasty
Anyone who then returns to the UK has to isolate for 14 days, under the government's existing rules.
There have been a number of reports that the UK will form "air bridge" agreements with certain countries to allow people to travel there and not isolate on their return - but a list has yet to be published.
Greece has re-opened its borders to some foreign travellers - but people are not allowed to fly directly to the country from Sweden and the UK until 15 July.
But it has been reported Mr Johnson travelled via Bulgaria to avoid this rule.
'Jetted off in defiance'
He said: "It might be an announcement that could be made by the prime minister, who could then explain his views on the fact that apparently his own father has jetted off in defiance of the guidance to Greece."
Referencing reasons given by Boris Johnson's most senior aide, Dominic Cummings, when he was accused of breaking the lockdown rules in March, Mr Carmichael added: "Maybe, I don't know, he just needed an eye test or something like that, but I think we would all welcome an explanation."
Answering for the government, Commons leader Jacob Rees-Mogg said: "I seem to remember somewhere in the Bible that the sins of the father will be visited on the son, but I don't remember it ever being the other way round.
"I think that the honourable gentleman is really fishing desperately to try and make any criticism of the PM."