During the calls, shareholders were asked questions about their investments in the football club.
The calls have been reported to officials at Parkhead who issued a warning to those affected, asking them not to reveal personal information.
It is thought the calls may be linked to 'boiler room' share scams.
According to the Financial Conduct Authority (FCA), these scams are run from 'boiler rooms', where fraudsters cold-call investors offering them worthless, overpriced or even non-existent shares.
The FCA say 'boiler rooms' use "sophisticated tactics" to approach investors, with some victims conned out of savings. Some have even lost their homes.
Victims of share fraud lose an average of £20,000 - with as much as £200 million being lost in the UK each year. The biggest individual loss recorded by the police is £6m.
Celtic were unable to confirm how many shareholders had been contacted.
A statement on the Celtic FC website reads: "It has come to our attention that recently a number of shareholders have received unsolicited telephone calls concerning their investments in Celtic plc.
"Shareholders should be wary of any unsolicited advice, offers or other communications regarding their shares and/or personal information.
"Following a recent increase in the prevalence of so-called 'boiler room' scams, the FCA and the Institute of Chartered Secretaries have produced a leaflet warning investors about unsolicited communications concerning investment matters.
"We continue to encourage Celtic shareholders to be vigilant."
Club officials are asking shareholders who receive unsolicited investment advice to get the correct name of the person and organisation, check that they are properly authorised by the FCA and report the matter to the watchdogs.