In a letter to The Times, Lord Ricketts said the British Prime Minister’s offer was “premature”.
Mrs May made the invitation when she visited Mr Trump in Washington last week.
A state visit would involve lavish displays of royal pageantry and a banquet hosted by the monarch.
Almost 1.5 million people have signed a petition calling for the visit to be cancelled to avoid embarrassing the Queen.
On Monday, thousands of people across the UK joined protests against Mr Trump’s travel ban on seven mainly Muslim countries.
Lord Ricketts, who was permanent secretary at the Foreign Office from 2006-2010, said it was unprecedented for a US president to be invited for a state visit in their first year in the White House.
He questioned whether Mr Trump was “specially deserving of this exceptional honour”.
“It would have been far wiser to wait to see what sort of president he would turn out to be before advising the Queen to invite him. Now the Queen is put in a very difficult position,” he said.
No date has yet been announced for the state visit. Such events often include a stay at Buckingham Palace hosted by the Queen.
The Times said Buckingham Palace had privately made clear it was unhappy at the perception the Queen was being dragged into a political event.
State visit to continue – Boris Johnson
Mr Trump’s controversial immigration measures prompted an emergency debate in the British parliament on Monday.
British Foreign Secretary Boris Johnson said the state visit would go ahead as planned, despite the petition.
The petition was started after Mr Trump issued an executive order barring Syrian refugees from the United States and suspending travel from seven Muslim-majority countries, stirring protests at home and abroad.
“Donald Trump should be allowed to enter the UK in his capacity as head of the US government, but he should not be invited to make an official State Visit because it would cause embarrassment to Her Majesty the Queen,” the petition said.
Earlier, Mrs May made it clear she would not consider any cancellation as she sought closer ties to Washington ahead of the UK’s split from the European Union.
British politicians want visit cancelled
Mr Johnson was questioned for more than an hour in parliament on Mr Trump’s executive order, declaring that his approach on immigration was not one the British government would take.
He called it highly controversial, divisive and discriminatory, but he defended the invitation to Mr Trump.
“It is totally right that the incoming president of our closest and most important ally should be accorded the honour of a state visit, and that is supported by this government,” he said.
A growing list of politicians called for the visit to be cancelled, including lawmakers from the ruling Conservative Party, opposition Labour Party leader Jeremy Corbyn and London Mayor Sadiq Khan, who is a Muslim.
“We must now rescind the offer of a full state visit for President Trump – until this ban is lifted. I don’t believe the people of London will support rolling out the red carpet until this happens,” Mr Khan wrote in the Evening Standard newspaper.
Mrs May’s Downing Street office signalled cancelling the visit was not on the cards.
“To be clear, the prime minister extended an invitation on behalf of the Queen – and she was very happy to do so. The USA is one of this country’s closest allies, and we look forward to hosting the president later this year,” Downing Street said.
The petition against the visit was the second-most popular ever on the parliamentary website, after one calling for a second referendum on membership of the European Union drew more than four million signatures last year.
A year ago, the UK parliament debated a petition calling for Mr Trump, then a presidential candidate, to be barred from the United Kingdom. It gathered close to 600,000 signatures before it closed.
– BBC / ABC