The Romantika, sailing under the Latvian flag, has arrived at King George V dock in Renfrew reports the BBC.
They added that the second vessel, the MS Silja Europa, will be arriving from Estonia in the coming days.
COP26 will be taking place from October 31 and November 12 and 25,000 government representatives are set to be in the city.
The First Minister gave a Ted Talk in Edinburgh ahead of the event saying that Scotland must "be careful" not to leave communities behind as it transitions away from oil and gas.
Ms Sturgeon stressed the supply of oil and gas cannot be turned off completely in the short term because that may lead to a spike in imports, as well as economic problems caused by mass lay-offs.
"We've got to be careful that we don't leave people and communities behind in that transition," the First Minister said.