Alex MacLeod won his Caithness seat in May's Highland Council elections at the age of 19, making him the youngest councillor ever in the Highlands. He became secretary of the SNP group on the council, but will now sit as an independent.
Now 20, he was the Gaelic spokesman for the SNP-led coalition which also embraces Liberal Democrat and Labour councillors.
He told The Herald he had resigned from the party while he worked with the police over the allegations. He would not comment on the charges.
Mr MacLeod, who spent 10 months working for First Minister Alex Salmond after leaving school, will still be able to attend and vote at council meetings. But, according to a council spokesman, he will no longer be able to vote on any of the committees he served on hitherto, because his membership had been as an SNP member.
It follows a complaint being made to Northern Constabulary in August by an unnamed member of the public concerning his conduct during the campaign.
It is understood the investigation is looking into allegations he did not declare staying in a hotel's flat in Wick during the campaign, which would have put him over the £1226 allowed in expenses.
An SNP spokeswoman said: "Councillor MacLeod has stepped down from the SNP until this legal process has concluded."