Cranney pleaded guilty to an assault by beating at Teesside Magistrates Court on April 28 following an incident on February 6 in Hartlepool.
Following the hearing, Cranney was given a community order for 24 months and told to attend a Building Better Relationships programme.
He was also given a victim surcharge of £95 and ordered to pay costs of £85.
Despite the guilty plea being only a week before the local elections, Cranney retained his seat as the prosecution only came to light just hours before voters arrived at the polling stations.
Confirming the suspension, Hartlepool Conservative Associate President Ray Martin-Wells said: “I found about the prosecution just before voting opened but it was after the close of nominations had taken place.
"As soon as I found out, I personally reported it to the Conservative Campaign Headquarters (CCHQ). I can confirm that Gordon Cranney has now been suspended and an investigation is now underway.”
When questioned as to whether in light of the prosecution and nature of the offence that Cranney should be allowed to take up his seat, Mr Martin-Wells said that would be dependent on the outcome of the investigation and that he “couldn’t comment any further until the investigation has taken place”.
News of Cranney’s conviction and the fact he was still able to stand for election has drawn fierce criticism from the Labour Party.
A post on the Labour Party’s Facebook page said: “Hartlepool Labour Party is shocked to learn that, as confirmed by the council, Councillor Gordon Cranney of Seaton ward was convicted of assault at Teesside Magistrates Court on April 28.
“As Councillor Cranney is a candidate in today’s (May 5) local election this information is clearly in the immediate public interest.
“We condemn violence towards women and someone with such a conviction has no place in public life.
“We are outraged that the Conservative Party would continue to allow Mr Cranney to stand as their candidate and demand that the Conservative Party immediately expels him.”
The post also called on Councillor Cranney to resign.
After finding out about the conviction, the returning officer for Hartlepool, responsible for overseeing electoral matters, has said the offences did not prevent Mr Cranney from standing for election or acting as a councillor.
Denise McGuckin, the returning officer, said: “I can confirm that I informed the President of the Hartlepool Conservative Party as soon as I became aware of this matter.
“Hartlepool Borough Council has also made enquiries of the public records held by the court and I can confirm that the offences do not prevent the candidate from standing for election and acting as a councillor.
“A person is disqualified if they have within five years before the day of election – or since their election – been convicted in the United Kingdom, the Channel Islands or the Isle of Man of any offence and has had passed on them a sentence of imprisonment (whether suspended or not) for a period of not less than three months without the option of a fine.”