The allegations relate to the purchase of laptops and IT equipment, thought to be worth £1700, bought with local authority money in September last year.
Fred Marinello, chairman of Granton Community Council, has also been accused of acting aggressively towards members at a recent meeting.
He denied the accusations and said the community council would be exonerated when the findings of the city council investigation were published.
Mr Marinello said: “There’s absolutely no truth in these allegations of financial mismanagement or anything else.”
“A full and comprehensive dossier has been sent to City of Edinburgh Council for investigation, outlining what went on and what was said and minutes for the last year if not more.
“The council is taking this very seriously, as they should. But we have provided more than ample evidence to show that everything the community council has done has been proper and within the rules.
“We have done absolutely nothing that would warrant such slanderous allegations.”
A statement issued by group secretary, Isobel Macdonald, said: “Due to fact that some allegations have been made against certain members of the community council and the community council in general and that an investigation is under way into these, it is prudent that we postpone the next meeting until the picture becomes clearer.”
It is understood three laptops had been purchased for use by office-bearers at Granton Community Council.
Claims of missing receipts, poorly recorded minutes, and the alleged forcing out of members from the local forum in conflict with constitutional rules are also understood to form part of the inquiry.
Expelled community councillor Thomas Brown, who was among those to lodge a complaint about mismanagement of funds, said he had first raised questions about inconsistencies in their financial records in May.
“I was asking questions about figures but I was never given an explanation.
“I was told that I was bringing the community council into disrepute for making false accusations. In September I was expelled for apparently not attending enough meetings.”
A council spokesman confirmed a probe had begun, but said: “It would not be appropriate to comment during an ongoing investigation.”
It is understood that events at a recent meeting, in which Mr Marinello is alleged to have acted aggressively has been captured on video and could form part of the council investigation.