The news came as the Kirk said another delegate to the event - a minister from South Sudan - had also been refused entry to the UK.
The Kirk said the Rev Sleiman had been barred from boarding a flight from Beirut because officials had not received approval from UK authorities.
The Lebanon-based pastor from the National Evangelical Synod of Syria and Lebanon will now miss the Kirk’s annual gathering, which opens in Edinburgh tomorrow.
The first female pastor in the Arab Christian world was due to have been granted a visa waiver from the British Embassy in Jordan after the Home Office made its U-turn on Tuesday.
A spokesman for the Church of Scotland: “We are satisfied the Home Office worked really hard to try to sort this out and they are looking at what went wrong.
“She was told she did not have clearance to travel, but her name should have been on the list.”
The Rev Sleiman’s visa application was originally turned down over concerns she would leave the UK at the end of her eight-day visit.
The Very Rev Dr John Chalmers, principal clerk to the General Assembly, said: “This has been a regrettable situation.
"Ms Sleiman was forced to make a two-hour journey from Beirut airport to her home in Tripoli last night after being turned back by officials.
"We accept the genuine efforts Home Office officials have made in recent days to overturn the original refusal to grant Ms Sleiman a visa.
“It is unfortunate the measures put in place were not sufficient to allow Ms Sleiman to board her flight.
“We had hoped to welcome Ms Sleiman to our gathering on Saturday, and hear first-hand the challenges facing the Christian community in the Middle East.
“It is a matter of real sorrow this will no longer be possible.”
The Kirk said the Rev James Makuei Choul, of the Presbyterian Church of South Sudan, had also been refused a visa, despite others from the church being permitted to travel to the General Assembly in the past.
Dr Chalmers said: “This is a particular disappointment to me, given the continuing efforts I am engaging in to build peace in this young and troubled nation.
“I would like to urge the Home Office to review its visa process to ensure the United Kingdom’s international reputation as a place of welcome is not diminished.”
The Kirk said the visa refusals were the first among hundreds of overseas visitors to the General Assembly.
It is now planning to invite the Rev Sleiman to a Women in the World Church event in Edinburgh in September.
A Home Office spokesman said: "Following a review of the case, arrangements were made to facilitate Rev Sleiman’s entry to the UK.
"These arrangements were relayed in full to the airline, but unfortunately Rev Sleiman was prevented from travelling."
He said of Rev Choul: "We do not routinely comment on individual cases.
"Each application is considered on its individual merits based on the evidence provided and in line with the UK's immigration rules."