The DUP said he had brought the party into "disrepute".
It is understood to be linked to complaints about Mr Devenney during last year's Westminster election when he was accused of canvassing votes for the SDLP outside a polling station.
Mr Devenney denied the accusation and said it was a misunderstanding.
It is understood the complaints relate to Mr Devenney asking DUP supporters to give their votes to the SDLP's Mark Durkan.
He now has 14 days to appeal his suspension.
In a statement, the DUP said Mr Devenney had been suspended with "immediate effect".
Mr Devenney is one of the DUP's highest profile politicians in Londonderry.
He has been a councillor in the city for 11 years and is a former mayor.
He replaced William Hay in the assembly two years ago.
Five months later, he stood down and was replaced by Gary Middleton.
At the time, Mr Devenney said he was stepping down because he wanted to concentrate on more local issues in the council.
It now appears relations within the party became strained shortly after that and came to a head on the day of the Westminster vote last year.
It is understood the DUP received a number of written complaints from voters who claimed to have been advised by Mr Devenney to vote for the SDLP.
The party investigated the complaints and has now decided to suspend Mr Devenney from the party.
He was informed of the decision in an email this week.
Because Mr Devenney has been suspended from the DUP and not the council, he is still entitled to take up his seat in the council chamber.
The BBC understands that he will not be involved in DUP council group meetings and will not be able to speak on behalf of the party.
Democratic Unionist Party councillor and former assembly member Maurice Devenney has been suspended from the party, the BBC has learned.