Parcel bombs have been sent to Celtic manager Neil Lennon, a lawyer and a politician.
Strathclyde Police have launched an investigation after the parcels "designed to cause harm" were sent to Lennon, Paul McBride QC and Labour politician Trish Godman, sources said.
They were initially thought to be hoax packages but analysis has revealed that they could have worked. A package addressed to Lennon was intercepted at the Royal Mail sorting office in Kirkintilloch, East Dunbartonshire, on March 26.
On March 28, a parcel for Trish Godman was intercepted at her constituency office and on April 15 a package was intercepted en route to Paul McBride, who has represented Lennon at Hampden during his dispute with the SFA.
A police source said: "They were viable devices designed to cause harm. We are treating the matter very seriously."
Mr McBride said he did not want to comment. Ms Godman, who is stepping down as West Renfrewshire MSP, did not want to comment either as police have advised her not to.
Police have offered safety advice to the intended recipients of the packages as well as to Royal Mail staff and workers in the mail room at Celtic.
It is the latest in a series of incidents targeting people linked with the football club.
Earlier this year packages containing bullets were sent to Lennon and to Celtic players Paddy McCourt and Niall McGinn, all three of whom are from Northern Ireland.
Scottish politicians have expressed their shock at the developments. SNP leader and First Minister Alex Salmond said: "Let us be quite clear - there is a major police investigation under way to ensure that the individual or individuals concerned are identified and apprehended, and then brought to book with the full force of the law.
"We will not tolerate this sort of criminality in Scotland, and as an indication of the seriousness with which we view these developments the Cabinet sub-committee met last Saturday to ensure that the police investigation has every possible support to come to a successful conclusion. We are confident that this will be the case.
"These disgraceful events should remind all of us who love the game of football of what unites us as a community.
"It is time to remember what we value in society, and unite to condemn those who use football as a pretext for their pathetic and dangerous prejudices."
Scottish Labour leader Iain Gray said: "I am shocked and appalled at this sinister development. It is vital, though, that people keep calm and do not let the situation spiral out of control as that would be playing into the hands of the extremists behind this vile act.
"It is outrageous that something like this should happen in Scotland in this day and age. Strathclyde Police must have whatever support they need."