Police Scotland are to step up patrols around mosques to reassure Muslims ahead of “Punish a Muslim Day” on April 3.
Deputy Chief Constable Johnny Gwynne said “intelligence assets” were “looking for signals” in the coming days.
The extra steps are being taken after letters were sent to several MPs in England earlier this month.
The campaign suggests people earn “points” on a sliding scale by attacking Muslims. No letters have appeared so far in Scotland, but the campaign has caused anxiety among Muslim communities.
At the Scottish Parliament, the first meeting of a cross-party group on tackling Islamophobia heard reports of children being scared, of adults considering staying off work, and even one couple considering cancelling their wedding on April 3.
Many speakers sought reassurances from the police, but also said they felt reluctant to give the hate campaign more publicity it case it spread alarm.
Senior police officers stressed there was no intelligence of any direct threat to anyone in Scotland, and the matter was “a risk” rather than a threat.
Their advice was for people to be vigilant and go about their daily business without being scared, but also to contact the police immediately if anything did happen.
Glasgow Labour MSP Anas Sarwar, chair of the cross-party group, said: “We recognise the fear and alarm the ‘Punish a Muslim’ campaign is causing, which has no place in society.
“An attack on one person living in Scotland, regardless of faith, is an attack on us all.
“Our advice to people concerned by this campaign is to go about your daily life, but remain vigilant, and we urge everyone to look out for their friends, family and neighbours.
“Any suspicious or concerning activity should be reported to the police, and we have received assurances from Police Scotland there will be extra vigilance around faith buildings and where there are large gatherings.
“Scotland must be united as one community of equals, and we have a duty to look out for one another. Only by working together can we tackle Islamophobia and all forms of racism and prejudice.”