A verse from the Islamic holy book was read in Arabic at St Mary's Episcopal Cathedral in Glasgow during the feast of Epiphany.
People from the local Muslim community were also invited to the service in an effort to build relationships between the Christian and Muslim faiths.
The passage said Jesus was not the son of God.
Criticism has come from almost all quarters of the church with the former Bishop of Rochester, the Rt Rev Michael Nazir-Ali, leading the condemnation.
Online complaints soon followed and the cathedral said it had reported offensive messages received to Police Scotland.
A spokesman said: "St Mary's Cathedral has received a number of offensive messages. These have been reported to Police Scotland.
"We are grateful to Police Scotland for their support at this time."
Police Scotland said it was investigating the offensive comments and did not tolerate any form of hate.
A spokesman said: "We can confirm we are investigating reports of offensive comments made towards St Mary's Episcopal Cathedral in Glasgow and inquiries are ongoing.
"Police Scotland will not tolerate any form of hate and encourages all communities to work together to ensure no-one feels threatened or marginalised."
