Selkorinn Choir sang in wind and rain outside a window of the ward where Groa Petursdottir is a patient.
She missed four of the group's performances in Scotland after falling ill.
Staff at the hospital kept the arrangements of the hospital gig a secret from her.
Patients from other wards, including the children's ward, were also able to watch the performance from their windows.
The choir had to leave for home after completing its Scottish tour without Ms Petursdottir.
She said of their surprise performance: "It was very nice of them and a lovely surprise. I was very moved."

The advance came as the US said it had conducted 21 air strikes near the town, slowing down the IS advance.
Tall Shair hill had been captured more than 10 days ago by IS militants.
Later on Tuesday, US President Barack Obama will host talks with military chiefs from more than 20 countries on how to combat IS in Syria and Iraq.
Correspondents say this is the first time such high-ranking military officials from so many countries have come together since the US-led coalition was formed last month.
In a separate development, Turkish warplanes on Monday bombed Kurdistan Workers' Party (PKK) rebel targets in Hakkari province near the Iraqi border, causing "heavy casualties", Turkish media report.
If confirmed, this would be the first major air raid by Turkey on the PKK since a ceasefire was reached in March 2013.
On Tuesday sources in the Kurdish Popular Protection Units (YPG) told the BBC that they had regained control of Tall Shair hill-top, about 4km (2.5 miles) to the west and near an informal border crossing.
In a statement the US military said Tuesday's air strikes had destroyed IS buildings and military vehicles.
The statement said the security situation on the ground "remains fluid with IS attempting to gain territory and Kurdish militia continuing to hold out".
The battle for Kobane, a predominantly Kurdish town, has lasted for a month and emerged as a major test of whether the coalition's air campaign can push back IS.
Two weeks of air strikes against IS targets in and around Kobane have allowed Kurdish fighters to slow the jihadists' advance, but Turkish and Western leaders have warned that the town is still likely to fall.
The Syrian Observatory for Human Rights, a UK-based activist group, reported that IS carried out three separate suicide bomb attacks.
One IS suicide bomber blew up an explosives-filled vehicle in the north of the town, near the border, while the second targeted an eastern area, it said. Later, a third bomber attacked a YPG position in the north-east.
The Observatory said it believed IS now controlled about half of Kobane.
Capturing the town, from which more than 160,000 people have fled, would give the group unbroken control of a long stretch of the Syrian-Turkish border.
Meanwhile at least 10 Syrian soldiers were killed on Tuesday in fighting against IS militants in the oil-rich eastern province of Deir Ezzor, the Syrian Observatory said.
The fighting took place near Deir Ezzor military airport, one of the last government-controlled outposts in the province.
Deir Ezzor has been a key target of air strikes by the US-led coalition fighting against IS.
An Icelandic choir has performed a surprise gig at Raigmore Hospital in Inverness where one of its members has been receiving treatment.
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Kurdish fighters battling Islamic State (IS) say they have recaptured a strategically important hilltop west of Kobane on Syria's border with Turkey.