Mohammad and Talat Aslam, who have five children, died in the incident near Medina on Wednesday.
The couple, from the Newlands area in the southside of the city, were part of a group returning from a pilgrimage to Mecca, according to Glasgow Central Mosque, which paid tribute to the Aslams as “popular members of the community.”
It is understood four other victims came from the Manchester area. The minibus was en route to Medina to visit the Al-Masjid an-Nabawī mosque.
The Foreign Office said it was supporting the families of the six deceased and helping others who were injured in the crash.
The group had just completed Umrah, a pilgrimage to Mecca, according to Glasgow Central Mosque, which issued a statement on its Facebook page.
It said: “A couple from Newlands, Glasgow were among a number of pilgrims who died in a tragic minibus accident in Saudi Arabia.
“We understand they had just completed the Umrah pilgrimage to the holy city of Makkah and were travelling in a minibus to visit the holy city of Madinah.
“We have every confidence in the Saudi authorities currently investigating the crash and in giving the dearly departed due dignity and decorum.”
It added: “Mr and Mrs Aslam were popular members of the community and are survived by their five children. We pray Allah the almighty grants the deceased a high rank in paradise and gives their loved ones strength and patience at this difficult time.
“We would kindly request the family be given space and time to grieve for their loved ones and to come to terms with their sudden loss.”
The Aslam’s niece, Yasmin Majid, was among those to pay tribute to the couple. She said she was “shocked” at their death and described her aunt as a woman who was “always so full of life.”
A spokeswoman for the Foreign Office said: “We are supporting the families of six British people who have sadly died following a road accident in Saudi Arabia.
“We are also helping several more British nationals who were injured in the crash. Our thoughts are with the victims and their families at this very difficult time.”
A spokesman from Haji Tours, which arranged the trip, said 12 people travelling in the vehicle were all related.